According to a variety of complaints made on Apple’s Communities website, it seems that many users are complaining that following the iOS 13.5 and iOS 13.5.1 updates, they have noticed that the battery drain on their iPhones is pretty bad. This seems to happen even when background app refresh has been disabled (which in theory should actually help conserve battery life).
One user with the iPhone 11 writes, “Update the software to 13.5 and battery drains super fast. I had a full battery and looked up something online for 10 min and it drained to 71% Can I go back to the previous update? Not happy with this at all!” For now, the only way to “fix” this issue would be to go to your apps and disable background app refresh.
This is not necessarily ideal as it means that for certain apps, you’ll have to wait for it to refresh whenever you launch it, instead of it having the information ready for you when you open it. However, it will have to do until Apple actually releases an update that will address the problem, whenever that may be.