Can an DM Terminate a players character from the game and make them make a new one? or would you class that as a unfair move?

I think the two key questions to ask here are

(1) If you do so, will the player have fun? That's the whole point of playing D&D, isn't it?

(2) Can you just ask the player? By all means if the player agrees. If you do that to me without asking, I would think you being rude and nor respectful, and (1)'s answer doesn't matter.

The real question is, why does the DM feel that PC is inappropriate for the campaign? The answer all depends upon the reason.

I don't think there's a blanket answer here. More context would be needed.

But I think this requires a lot of discussion and negotiation between the GM and the Player, to figure out what the core problem is, and fix that.

My gut reaction is no - unexpected, unilateral removal of a Character by the DM is ( at the very least ) rude. If this Character is such a problem, why did the GM allow it in the Party to begin with?

Quote from Vedexent >>

I don't think there's a blanket answer here. More context would be needed.

But I think this requires a lot of discussion and negotiation between the GM and the Player, to figure out what the core problem is, and fix that.

My gut reaction is no - unexpected, unilateral removal of a Character by the DM is ( at the very least ) rude. If this Character is such a problem, why did the GM allow it in the Party to begin with?

 Well sure, but the way they said “terminate” might mean the PC died. That’s not “unilateral removal” so to speak. So if the Kit_Ara_Liadon comes back and says “(The DM said)/(I say) the reason the PC is no longer appropriate is because they died” then I gotta go with yes on that one. Or maybe they didn’t understand what a 50-flying movement really meant when they okayed an Aarakocra, then you’re probably right and a conversation might be more in order. Worse yet, maybe they okayed a Mystic figuring that since WotC wrote it it would be okay without really knowing. That would be unfortunately rough for everybody.

I feel that if a Character merely died in the course of an Adventure, we wouldn't be having the question come up. It's not impossible, but I think it unlikely.

In any case - I did interpret the OP meaning that the GM was removing the Character for meta-gaming reasons, or table issues - and my answer is only valid under those assumptions. If the situation is different, so would be my answer.

Good point. I guess we’ll have to wait and see. 

Can the GM do so?  Yes.

Is it a good idea to do so?  Generally not.  The real question is what's going on that makes you want the character out of the game?

 Assuming that Kit_Ara_Liadon is the player based on post history, I suggest talking to your DM. As has been said, yes the DM can do that, but it's bad form if they didn't give a reason. But even so, I'd rather a DM do it straight up like that as opposed to throwing in way too high CR enemies and have them target only me. 

Maybe I'm just suspicious but the Op said nothing about the GM not giving a reason, he just said the GM terminated the character from the game.

As others have said it depends on the situation but there are definately circmstances where it is a right thing to do:

Lets say a PC chaotic evil (maybe with CN on the chaacter sheet) and goes around stealing from the other characters, insisting that he gets every magic item they find and otherwise ruining the fun for the rest of the group.  The rest of the group have said they have had enough of him and they want nothing else to do with him but he continues to stalk them and interfere with their adventures.  The rest of the party are basically good and don't want ot flat out murder the PC.

The other PC go to the DM and say they are not having fun with this annoying PC ruining their game so the GM goes to the player and says his character is no longer going to be in the game and asks the player to create a new character that is more of a team player so everyone can enjoy the game.

Thanks to everyone who reply and yes I am a player my Dm has killed five of my characters off already with no reason behind it and it is making over people not want to play anymore. Also thanks for your help with this matter as I did enjoy D N D before the DM change the rules of the whole thing to what he wants. With no reason. 

Just remember that bad D&D is not better than no D&D.  The game is about having fun and if you're not, and it's for reasons you can't resolve by talking to the GM or other players, there's nothing wrong with quitting the game.

bad D&D is not better than no D&D

This. Better to not play D&D than to play it and be miserable. Fun is why we do it.

FIVE of your characters?!?!  Just yours alone, not including other players?  Holy hell, that's ridiculous!

I don't know what the situation here is so I can't be a fair judge and say exactly where the problem seems to be, but regardless if things have gotten to that point then it sounds like you and this DM need to part ways, pronto!

Quote from Mezzurah >>

FIVE of your characters?!?!  Just yours alone, not including other players?  Holy hell, that's ridiculous!

I don't know what the situation here is so I can't be a fair judge and say exactly where the problem seems to be, but regardless if things have gotten to that point then it sounds like you and this DM need to part ways, pronto!

 Well $|-|¡+

Even I haven’t killed 5 PCs on the same player in one campaign since AD&D 2e back when that was normal for everyone. And I throw crazy stuff at the PCs in campaigns I DM.

Either the OP plays suicidally (Leeroooooyyyyyy Jenkins!!!) or their DM is a sociopath collecting PCs as trophies instead of IRL victims. 

Yeah 5 is an awful lot.

I mean it happened to me back in 1st edition days, but back then there were only 2 of us so we each made up like 5 characters each so yeah you lost multiple characters but it's because you WERE the whole party....

First campaign I played in back in 2e there were 3 players and a DM. Each player made 3 characters, 9 went in, 4 walked out of a partially cleared dungeon. Body counts were high back then. But not in 5e, not usually.

Quote from IamSposta >>

First campaign I played in back in 2e there were 3 players and a DM. Each player made 3 characters, 9 went in, 4 walked out of a partially cleared dungeon. Body counts were high back then. But not in 5e, not usually.

Yours was about the same as mine. 2 players, 5 characters each. 10 walked in. 5 walked out.

And that was after a Ring of 3 Wishes and at least one Raise Dead scroll.

Quote from BioWizard >>

Quote from IamSposta >>

First campaign I played in back in 2e there were 3 players and a DM. Each player made 3 characters, 9 went in, 4 walked out of a partially cleared dungeon. Body counts were high back then. But not in 5e, not usually.

 

Yours was about the same as mine. 2 players, 5 characters each. 10 walked in. 5 walked out.

And that was after a Ring of 3 Wishes and at least one Raise Dead scroll.

 When we came out to get reinforcements (roll more new PCs) and resupply the first thing we bought was a Pole (10-foot).

Our first death came after the level 1 thief checked for traps on the first chest we found -- he checked! Found no traps. So (since it was his turn) the druid opened the chest, pricked his finger with a poison needle, save-or-die, fail.