IPhone 5s screen went completely black but it's still on?

I know that the phone is on because i hear the noises for notifications and plugging in the charger. I looked this problem up and found that a solution that worked for most people was to reset their phone by holding down their home button and lock button at the same time, but my home button has not worked for a while. Is there any other way to reset it or fix the screen?

No

Yes, taking the phone to an Apple store or a cell phone repair shop that works on iPhones, and get it repaired. If YOU could have taken care of this yourself, you would have done it already.