Hi there, welcome

Hmmm, I’m thinking a couple things might help. First would be restricting his space, possibly to his crate plus an x-pen (or two!), and make sure the only soft things are in his litter box. Sometimes when buns have too much space too quickly they decide the litter box is too far away. Having him in a smaller area might help him get organized. Making the litter box as enticing as possible with lots of fluffy hay can also help.

Also, buns often like to pee on soft things, and things that smell strongly of humans. The couch and rugs might fit this category.

The timing of everything also makes me think it might be related to his neuter somehow. 5 months is a bit young (usually males are neutered at 6 months), so is there a chance that his neuter was incomplete?

When he pees, is it large puddles, or dribbles? And when he poops, is it large piles, or single pellets around? Large puddles and piles signals that he just doesn’t feel like going to his box. Small poops left around is more territorial. Dribbles of pee could be a urinary infection or some other medical issue. I had a bun with dental issues that had TERRIBLE litter box habits. Pain can manifest in a range of ways!

So, I know that was a lot, but I would start by restricting his space and see if that helps. If it seems like something medical might be contributing, have a rabbit savvy vet examine him.