What does "doing five to ten for one thing or another" mean?

As @FumbleFingers said, it means that their boyfriends are doing between 5 and 10 years in prison for various crimes that they have committed. "One thing or another" or "one thing and another" is an expression used to cover various unspecified matters or things, in this case various crimes.

It is referring to the prison sentence that someone received for some crime. Almost all sentences have a minimum and maximum length. The shorter is the length of time that they must stay in before they can be eligible for parole, but there are other things that can be done to get them out earlier. The longer length is the time they will be released if they never made parole (for that particular sentence).