Since you can't know the extent of the damage, trying to repair it yourself is probably not worthwhile. You might end up having thrown a lot of money into it, but still not working.
You should get it check out by a phone repair man first. If he can't do nothing for you then you should go ahead and buy a new s5 aka the bandaid phone.
As Josiah implied, you won't know whether it pays to repair until you find out how much it's going to cost to repair. A new screen or a new motherboard isn't as expensive as a good used phone. If more than one major thing broke, it may not pay to fix it.
My friend has the same problem. His galaxy s3 screen won't turn on but the touch keys on the bottom of the phone will light up. He said some led light that makes us see the screen has broke inside his phone. If you know how to disassemble your phone, fix the problem and assemble it back, then you could go that route. That piece might be cheap, but if you broke the digitizer (a piece that makes phone touchscreen) then that will cost you some $$. I recommend going to a repair man because that will cost you less than buying a new s5.
Sent from Mr. Mobile Nations using a Samsung Galaxy S5!