I thought possible re-downloading lightroom might solve my first problem.. It did not. However now even though I've already bought lightroom 5 it is asking me to put in my serial number or continue with the free trial. When I put in my serial number it states that I'm using an invalid serial number. I wish I could get on the phone with someone and get this straightened out but this seems to be my only option.
There's no link to your first problem so not sure how that might affect or relate to this one but I might guess that if you've re-downloaded LR you've very possibly downloaded the CC version and need the standalone version (which is harder to find).
Uninstall the version you have and go here for the standalone one:
If this is not he case then we'll need more details.....