The How-to for the 5007 is here; one thing I need to add is that you can secure the drive by putting screws in from the bottom of the case through the mounting holes.
If your current drive doesn’t have a metal bracket around it, you can probably get the tray open by taking off the top plastic cover to get at the mechanism. (It’s likely that it’s not opening because of a deteriorated rubber belt.) It’ll be more difficult to do a clean replacement if you can’t get the tray to open.
I’ve had the best luck in general with the earlier Liteon drives as replacements; I like the 1633S and had trouble with a 1693S and a 165P6S (which also tends to have belt problems). But all of these earlier drives are hard to find now, of course.
Also, you can easily try out a drive just by plopping it on top of the bad drive and hooking it up to the power and IDE cable. Remember to unplug the unit first or you risk blowing the fuse (or worse) - the power supply is always on when it’s plugged in.