@ethanquincy There should be no reason why not, however the question here would be more how to do it than whether you can (finding the correct guide or adventuring yourself) I've asked the author of this post if he could add a full view of the back of the machine, without the cover blocking the parts, to see if the HD is easily accessible. Another issue I could see is Windows license restrictions. You might want to look into Linux, depending on your use of the computer.
Please see @flyingdutchman 's answer to this question: How to get access to fix the optical view finder lens? You will have access to your viewfinder, and will be able to assess whether it needs replacing or just popping a lens back in.
From your pictures it looks like it's only your screen that is damaged. If the board was damaged it would most likely not provide any video to the screen. Replacing the screen is not very difficult, but will probably run more expensive than getting a newer iPhone 5 or 5s, as this is an old phone. A quick search on this site showed no inventory.