Fuji S5500 camera and lens

It seems clear to me (and probobly to you as well) that the solution is to tighten up the lens. regarding the question if you can do it by yourself, i think the answer is probobly no. on one hand, there's a chance it is a very simple problem that only requires tighting a screw, however, i wouldnt risk a 500$ camera for a 30$ repair.
my advice will be the local repair shop, if price is too heavy for you, and camera functions fine as it is, you can live with it for a while, just keep in mind it can get worse.