Most 1-9 twist 223/5.56 barrels will shoot up to a 75 grain bullet,but it will depend on the length of the bullet. A 75gr BTHP is shorter than a 75gr A-Max,and shoots great out of my Savage 12,but the A-Max's don't fair to well,the twist rate doesn't stabilize them very well.
Since your shooting an AR,the 75gr BTHP will be the largest bullet that you can load to magazine length. A 75gr A-Max would have to be shot like a single shot rifle.The max length for a magazine is 2.260",and the 75gr Amax should be around 2.390"
I shoot them out of my 1-8 twist RRA varminter,as well as 77-80gr match bullets,but it is a single shot rifle when I do.
55gr-69gr bullets will shoot great out of your rifle,and all will fit in the magazine without any problems.