beginner help with tiny weights

[some_stars]

hi :D I have admired this comm for some time, and I've been meaning to get back into strength training for ages, and since I will be starting school in a couple months and have access to a nice gym, and because I've gotten back into swimming a lot, this seemed like a good time. I'm moving cross-country in two weeks, so I just got two five-pound weights to work with a little until whenever I'm able to start using the gym.

Basically, what can I do with them that won't hurt me, especially my shoulders or knees, and will be useful for swimming? I used to lift weights but that was like ten years ago, and I'm pretty weak now. (I tried a 15-pound-equivalent resistance band first and had to return it.) I also need to start working on my core, because all those muscles are basically completely atrophied, but my problem with that has been that because I'm SO weak in that area, even when I try gentle exercises I end up using my back and hurting it. So I guess I also need tips on how to make sure I don't do all my lifting with the wrong muscles.

Also: how do I work my lower body without using machines, but without using my entire body weight as the weight?