Can my iPhone be repaired? Dented back, bent frame, not powering on. (Read description)?

I dropped an 80 pound dumbbell on my iPhone 5s it dented the left side towards the top the frame is a bit bent. Screen is not cracked. The phone is not turning on though. I also have not backed it up for about a month, is there anyway I could back it up? And is there anyway I could get it working?

You can't back up a non-functional iPhone.

As to whether it's repairable, then as long as the main motherboard is undamaged every other part is replaceable but it becomes a question of whether it makes economic sense as used iPhone 5s models can presently be purchased fairly cheaply.

You'll only find out whether your phone is scrap or not by taking it to a repair shop. They can dismantle the phone and check the motherboard for damage. Although the screen isn't cracked expect to have to replace that as well.

If you're practical and have experience of repairing electronics then you can look out for a cosmetically good but non-functional iPhone 5s. If you get it cheaply enough it may provide all or most of the spares you require, but some of those spares may be useless if it's been water-damaged.