Depending how complaint prone your neighbours are obviously. Low frequencies are what bother neighbours usually the most, since they retain more energy while traveling through walls and thus are the most audible (unless your walls are really thin, then higher frequencies will bother too). That being said, even though 5" and 8" monitors are quite full-range-ish, they aren't exactly meant to extend beyond 50-80Hz as they're meant to be coupled with a subwoofer when the application requires one (like movies and games, for instance). You'll always benefit from a separate subwoofer with bookshelf speakers. Your current subwoofer might be only 5.25", but it's also tuned to resonate at a lower frequency so it might actually be more annoying to your neighbour than a pair of 5" monitors. The speakers shouldn't really annoy your neighbours any more than your present set, if you use them equally loud. I would be concerned when you get a 10-12" subwoofer though.
But yeah, expect it to cost a sweet deal more if you want to get higher clarity in the mid and high-ranges in the form of actual speakers, but also want the bass-department to dislocate your jaw. It's going to be about few hundred quids for a sub too.
Then again, when I first got my 8" studio monitors I was like holy crap I'll never need a subwoofer, because I had gotten used to a set of 3" actives in the form of AudioEngine 2 clones, and a 8" subwoofer. But then I got a subwoofer later for the 8" monitors too
Hunger grows while you're eating with these things, so you can either settle with some satellite set that's easy to position and set up, or bigger heavier speakers that you might enjoy a lot that are also going to cost a good deal in the longer run. I bet you'll like them anyway, it's more of a question of principle do you want to seek high fidelity or just want a replacement for your current speakers (I don't feel like I'm helping you at all contradicting myself in every other sentence tbh