How much does it cost to repair an iPhone 5c?

My iPhone 5c does not have a cracked screen, but it does have a lot of scratches and cracks on the bumper (or whatever it's called), the sides of the phone. I also recently dropped my phone and landed on the power button so now it's slanted and hard to press down.

Would I be able to repair it, or replace it with a new one? How much would it cost?

Apple does not cover accidental damages such as dropping a phone or spilling water on it. If it is a technical issue such as internal problems that have no evidence of tampering then it will be free, otherwise it should cost upwards $100 for a screen replacement and $269 for a replacement.

I hate the 5c mine cracked today. Go to the apple store and say it's something technical wrong with your phone such as the battery won't charge and they will give you a brand new one for free make it sound convincing that's what I did

I think it is better to replace it, As you said scratches and cracks on the bumper are not able to fulfill it, They will check it and tell you the amount, how much you will have to pay to replace it. Atleast you have to pay half of the actual price.

If you trust them go with 3rd party repair shops, markets usually have people who can repair your phone. It cost me £30 to replace my screen on my iphone 4s compared to the £120 apple would have charged me! I also got it back the same day!