So I've been a DM for a while and most of the time my players are able to kind of band and form a group identity together on their own. My newest party however are very new to the game and don't know how to roleplay very well yet or how to develop the backstory of their players much.  Right now they kind of feel like very separate people who are only adventuring and going along with objectives because I am giving them quests to do. I want them to get more comfortable in character and have their characters bond a bit. Are there any tip on how to get them to bond a bit as characters?

Talk to them and ask them questions about their character. My favorite question to ask is  "what is the core or heart of your character"  The main idea, the essence the key component. Everything else can kind of flow from there. Once the players figure out the core, I would recommend using a character background template such as the "Heroic Chronicle" found in Explores Guide to Wildmount in order to build a skeleton and muscle around that core and have a more robust background. This way you can use their beefed-up backgrounds and tie them into the campaign.

As for roleplay. You need to provide Reinforcement for engaging in roleplay. Award inspirations for roleplay. Allow players to solve problems through roleplay without needing to roll the dice. Maybe have the players gain access to items or spells by roleplaying. Maybe have a few sessions without combat or the possibility of completing quests without combat. 

I really want to see people’s responses to this thread, but I can’t figure out how to subscribe without commenting. My players are having this same issue.  I’ve tried to encourage them to talk to one another, but 3 of the 5 are very shy.  Obviously I’m not going to force them; I’m just hoping to see an idea I haven’t tried yet.  I’m sorry for my non-helpful comment!

Some people just aren’t good at, and don’t really want to be. That kind of storytelling, rp heavy game isn’t fun for them. So first, make sure you aren’t forcing them to do something they can’t or don’t want to do. 
That said, as much as I’m not much of a critical role fan, maybe have them watch an episode or two of that (or some other stream). It could be they need an example of a way to play, and see if they might want to incorporate it into their own playstyle.

I don’t think loads of backstory is required to have characters bind together (look at the Fellowship of the Ring). In fact, it can drive characters apart as much as it brings them together, since everyone gets focused on their own little story. I’d suggest engaging them individually with an NPC: something as simple as the barkeep asking each of them what they’d like to drink can go a long way.

Or, for a little more depth, have a local bard appear hoping to write a song about the party’s greatest exploits. The twist: he says he’ll only listen to what the characters say about each other, not what they say about themselves. Cheering on each other’s heroic exploits is a great way to develop characters and group bonding!

My typical appoach for my players (I only do in-person games with friends), is to have a session 0 to get the basics across (expectations, limits, house-rules, campaign world & some basic lore, etc.). One of my requirements at my table is, that I expect from my players to actively further plot and events and that I expect them to cooperate somehow. I will not accept if players only want to do their own thing, because this game is a party based RPG. Furthermore, I ask my players to find some of them who like to team up and come up with a reason, why they already know each other. This is not a requirement, but often it helps and is well received by my players.

After that session 0, I collect the character builds and background stories of all of my players, doing something like individual sessions 0.5 where I discuss specifics of each character. If players teamed up, I do the session 0.5 with both or all of them.

Then, when all character builds and background stories are available to me, I start constructing the opening scenario leading into my campaign, specifically tailored to fit all the characters in. I try to create events, that bring all the characters together and gives them a common purpose.

Typically, this is enough to first create cooperation and keep the whole party engaged with the plot. Mostly, bonding happens by itself even with limited roleplaying.

Edit: Just to clarify, common purpose is not just a quest, but some plot hook, that gets the characters personally invested. And the background I want from my players does not need to be that deep, but I need and expect at least something.

Have the NPC assume that they are friends and ask one character to bring a message (or something) to another player. This can be both plot-related stuff or something trivial just to get them going.

If a player has a familiar or a mount, have someone approach one of the other character with an offer to buy it or just to complement it. "Hey, you know that dude with the pet monkey, right? Can you ask if they are willing to sell it?"

NPCs can also just start chitchatting with them while they get their quests. "Wow, you're really good at this. Have you been working together for a long time?" or "I'm going to have to give you payment in the form of a cheque, who in your group is handling the finances?" or perhaps just "Did you grow up together?"

If they have a regular employer and are working on a quest to quest-basis you can also do stuff like the employer offering them something that they need to talk about. Like the choice of a magic item that might benefit one of the party members instead of money. Give the players the chance to discuss amongst themselves what they would prefer.

Whatever you do though, make sur ethat you as the DM give every player a chance to speak. Ask them directly what they thing of the thing being discussed. Both in-game and out of character. For example, let's say that the employer offer them a magic wand that allows the party's cleric to cast cure wounds on people instead of a bunch of money. Let the players talk amongst themselves for a bit and make sure you ask every player what they think. Then you can have the employer ask the group, perhaps turning to on of the characters who didn't speak up as much during the initial conversation and ask what the group's decision is.

From a mechanical point of view, it might work to give them tasks which require teamwork, and also tasks that require splitting up. How the party splits will probably highlight if some of the characters are becoming friendly (barbarian always goes with rogue, for example) but if they always say "we'll put you and you together because your fighting styles match..." then they are still just splitting based on mechanical means.

Roleplaying can be encouraged by questioning how they are doing something. - "I ask the guard to come with us." - "How do you ask them? do you do so pleadingly, or bossily? how do you present this to the guard?"

The players don't have to do voices or acting, or even say the exact words if they don't want to, but they realise that they are not playing a monotonous robot* and have different ways to present a statement. After a couple of sessions of asking this sort of thing when it's relevant, the players will start pre-empting this sort of thing and state/act/whatever their method of delivery as well as the mechanical acts. Keep this up when they are talking to one another and it will start to build up a dynamic between them. Try to encourage them to have tactical discussions in-character rather than out of character - no saying "you have 4 spell slots left and he has loads of health so you need to do most of this fight". If they say this to someone, interrupt before they answer and say "so what is your character saying then?". Try to keep them in the game rather than keeping popping their heads up to discuss things.

*warforged designed as monotonous robots excepted

It is perfectly fine for them to feel that way, a group who are brought together for a love of coin is a valid reason to be a group together. I would also not push the roleplaying element hard if they are learning the game, maybe talk to them out of game, instead of making them roleplay conversations ask them to describe in the 3rd person what there characters might have talked about round the campfire, what they have discussed. Maybe ask each player to write down 3 questions that they have for the other players and get them to ask them, simple things like where are you from, who where your parents etc. 

Roleplay does not have to take place in first person perspective to be fun, I have run groups who’s entire process was describing what characters did or said as opposed to being the character in the first person. I have run groups who  had there in group conversations as themselves between players round a table. Where is your character from, what are they willing to tell the group now they know us a little bit. 

This can be a stepping stone to more involved first person roleplay, or it may never develop beyond this point. 

Video games, among other media, often handle this by each character having a side quest that goes into their backstory. As you go through the quest you learn more about the character and feel closer to them. This is a great route, especially if you can weave the backstories together a bit.

That's is a really good idea I was thinking of doing down time in our next session so Ill give the bard idea a try. That is a really fun way of doing it.

 Admittedly I haven't gotten a chance to DM yet, but as someone who's run some forum roleplays and been roleplaying for over a decade something that can easily drive interactions beyond an outgoing character personality is the goals the characters have. You can have an anti-social loner character work well because they have to interact with people to get what they need. If all the characters right now only want money, maybe ask them to come up with a reason they want that money beyond being able to survive, and how badly they want money (would they do anything for a piece of copper, or is 10,000 gold not enough payment to punch an old lady?). Perhaps they need funds to pay someone to heal a cursed family member (side goal could be finding who cursed them!), or their motivation is feeling emotionally secure by amassing as much gold as possible after growing up a street urchin. The first person is probably caring and giving and would check up on their fellow party members, the second probably desperate and neutral-aligned at best but could go out of their way to network or push the party to take new jobs. I also always like when my DM has two people take watch at a time during long rests so they can talk about themselves or what's been going on as well. An npc casting zone of truth on the party for some reason could lead to some interesting discussion.