You can get rid of THAC0 if you just use this simple rule: roll d20, add the opponent's armor class (plus your own to-hit bonus if any), and a result of 20 or better is a hit.
3E's Base Attack Bonus was mechanically identical, but expressed in an easier-to-understand way. Briefly, they rearranged things so that higher numbers are always better--having +1 armor no longer means you subtract 1 from your Armor class.
I'd make a silly wager that the net time saved by using 5e rules would outweigh the cost of learning them.