I am starting as a lvl 1 PC and I wanted a floating sword with me is there anyway I can do this between lvl 1 to 5 ?

One option to do it RAW would be to make an Artificer character, then use an infusion to create an Homonculus Servant, which you determine the appearance of, and can fly. It can also attack for force damage, which means it fits pretty well for reskinning something into a flying sword.

I am not hugely familiar with the Hexblade warlock, but being a magic-based-sword-wielding class, it might offer some options which suit.

Alternatively, you can discuss this with your DM to see what they might allow you to find along the way - Oft times, by telling the DM what your character wants rather than asking for it to be theirs now, you'll find just such an item appearing along the way!

I think it's possible to play as an Echo Knight Fighter and reflavor it to be just a floating Sword instead of a full-on shadow copy of yourself. It's kind of a sloppy reflavor... it doesn't fully explain how and why you can swap places with the sword, or why it's considered Medium Sized, but it's a quick and easy way to make melee attacks at range.

EDIT: Also, I can't believe I didn't think of the spell Spiritual Weapon. It's a 2nd level Cleric Spell, although it is also learned by Conquest Paladins at level 5. I don't think there are any other classes that get access to the spell natively, although a Bard's Magical Secrets can unlock it.

Quote from ThorukDuckSlayer >>

Alternatively, you can discuss this with your DM to see what they might allow you to find along the way - Oft times, by telling the DM what your character wants rather than asking for it to be theirs now, you'll find just such an item appearing along the way!

 This is probably the best option. You're probably going to be able to get much closer to what you want by getting the DM to buy in.

There are two things that will make your request more palatable:

• You shouldn't get a big advantage out of it. If you're trying to get another attack for free out of it, or get two-weapon fighting plus a shield, you're not likely to get it. If you just ask for a sword that floats around with you, but you still need a free hand to make it attack, that's more likely.
• If it gives the DM some fun of their own. A magic sword that floats around you? Not that fun. An intelligent magic sword with a clashing personality and its own agenda that floats around with you, and you can't get rid of? Much more fun.

That said, another option would be Pact of the Blade Warlock. Your pact weapon is the sword. Instead of stashing it in an extra dimensional space, it floats behind you. Your Eldritch Blast gets the chrome of the sword streaking out to strike at your enemies.

Quote from TransmorpherDDS >>

EDIT: Also, I can't believe I didn't think of the spell Spiritual Weapon. It's a 2nd level Cleric Spell, although it is also learned by Conquest Paladins at level 5. I don't think there are any other classes that get access to the spell natively, although a Bard's Magical Secrets can unlock it.

This is the best RAW way to go about it. Nothing says the weapon can't be a sword.

There is the dancing sword.  Whether your DM will give it to you at an early level is another question, but it is a possibility.

Quote from Mezzurah >>

There is the dancing sword.  Whether your DM will give it to you at an early level is another question, but it is a possibility.

 You could also go with the monster a flying sword as a familiar. If OP has find familiar, then they could ask the DM to make an exception and let them summon that. However, it does raise the same problem as that magic item, since a flying sword is a pretty powerful monster for a level one familiar.