iPhone 5 Crashes & Restarts Repeatedly

Hello, my iPhone 5 has recently started crashing and restarting when it reaches about 75% charge. When it restarts, the battery reads about the same percentage as it did before it crashed. When I try to open an app, it crashes again. On the second or third time, it doesn't restart, and simply shows a flat battery symbol. If I put it on to charge at this point, it starts up and shows about same battery percentage as before it first crashed.

Does anyone have a suggestion as to what could be wrong? I don't want to go to the trouble of replacing the battery unless I know that that's the likely culprit.

Many thanks in advance!