I started doing a workout routine which has bench presses in it (I've bench pressed before) and I was wondering if bench presses would help increase the number of push-ups I can do. I've always been pretty weak on my upper body and it would be rare if you can see me do five push-ups perfectly without stopping.
Bench Press *CAN* help if your muscles are that weak, but it's more like Press-ups help Bench Press, from my own personal experience, back when I could do 78 Press-ups I shot up in Bench Press strength
Yes bench presses will increase your push-up count without even ever doing push-ups. This might be more difficult however if you're already in the high-end of push-ups, at this range cardiovascular endurance is also a big factor, and not just strength (if you're doing 40-50 + pushups) but in your case since you can rarely do five, the main problem you have is with strength, and bench press will develop your pressing power better than pushups can. so yes it will help you immensely.
