Finally decided I couldn’t afford an iPhone 7 after much deliberation, so I took my 5s in for a new battery. When I got back, they informed me they’d broken my screen trying to replace the battery, but here was a brand new 5s for the price on the battery replacement. Seems like a win to me.

Can vouch for the cpu throttling with worn batteries- this new one is much smoother & faster with a fresh battery.