Could always (if possible I guess it might be), allow the user to change the Title only so they could update it to [Solved] instead of closing the topic. All editing rights for topic etc, would still remain appropriate to membership level though.
That does rely on the users to actually do that, which many won't bother/remember/come back to the thread after their question is answered.
Sometimes there is more than 1 solution to a tech problem and in your or any scenario, personally, I would go through all 5 threads and make a uniformed decision. The feature will mainly promote search engine hits, where someone may find an answer useful or not and along. You can say this is true even without a solved button but I think that sometimes promotes people to sign up and involve themselves in a discussion rather than glean over an answer, never to return again.
Have you ever worked full-time and looked after an incredibly popular forum? I know I've done it with a full time job on a forum that wasn't even a quarter as popular as this and you just don't have the time to do such manual grunt work.
I don't think the influx in people signing up would be really worth it, to be honest. You get traffic by having content, you keep that traffic by having great content.
Add '[SOLVED]' to the title and leave the thread open. Job done. Or leave it, it's not that big a deal - are there any other mods who have an opinion?