There's a 5E supplement at DriveThruRPG called Into the Unknown that tries to model the B/X game. The game does gold for XP and combat for XP, along with higher xp requirement for gaining levels (e.g. it took 1,250 xp to get to 2nd level). The game is broken down into 5 booklets costing about $5 each in PDF.
Aaanyway, my point to this post is to provide a potential way to calculate xp through Combat using that game's method:
For every 1 H.P. damaged caused, the player gets 5xp.
For every 1 H.P. lose, the player gets 10xp.
I've used it before as a DM and, yes, it was slightly fiddly but still manageable.