Op I have every sympathy with you and I am probably going to attract some criticism posting this, but having raised two dc, one of whom was challenging, I would say that the fact that your ds felt comfortable throwing ketchup around in a stranger’s house, before you stopped him doing it, is indicative that:
~either he isn’t used to having to comply with simple age appropriate boundaries
-he is one of those enormously energetic children who need shed loads of exercise every day before interaction with others otherwise he gets completely overwhelmed and excited
-or he may be struggling with ADHD or something similar?
Or a combination of the above!
Whichever it is in your shoes I would be tackling this with with different approaches all at once:
~start upping his physical exercise daily taking him swimming, buying him a bike, signing him up for minis football? Or karate, or whatever it takes!
-start trying to redirect or funnel his behaviour in to something instructive or constructive eg get him a spade, a big bag of compost, a mini wheel barrow and ask him to dig a hole or build a flower bed. Or put books in to a tethered book case. Or give him some actual simple jobs like washing windows he can reach. Four year olds at my DD’s riding school used to be able to feed the mini Shetlands, pick up poop, lead horses, brush them and tack them up - all under careful supervision of course - but my point is that five year olds can do more than you think, and quite complicated things too, given clear boundaries. Some children need to be constantly challenged with things slightly above their immediate ability. If he is throwing trucks around that tells you immediately that he needs something more constructive to do!
-start imposing some quiet time in to your daily routine so he he gets to know that say after school he can babble away, but then after tea needs to do a quieter activity while you do other things nearby. It’s about getting used to entertaining himself for short periods of time. Start with five minutes and build up. Reward at the end.
Every child needs to learn this skill and not saying you are doing this op but some parents tend to switch between full on attention to screens and forget about “playing by yourself” in the middle which is a vital skill for school.
-take him to the doctor and have a wee chat about how much sleep, how much physical activity is average this age. Tell them about your struggles and that way it’s on record early on, should you be seeking an assessment later on.
-out-sourcing? Can you afford an active baby sitter to take him out for a couple of hours one weekend morning or afternoon? Then at least you can have one predictable period of time per week when you know you can get relief from his constant noise and activity, and something to look forward to.
And fwiw, sorry but maybe think about imposing behaviour boundaries more strictly? You may find he is happier this way when things are clearer? He may stop testing you?
If my dd had thrown ketchup around at a stranger’s house then they would have been removed and taken straight home. No hesitation. And it would have been explained later on when she was calm that she would not be attending any parties if she couldn’t demonstrate that she knew how to behave properly in someone else’s home,
And the next day they would have been marched to their friend’s door with a bunch of flowers and a picture they had drawn with the word “sorry” written on it. No hesitation.
Maybe others think that’s harsh but is it possible you are speaking to him too nicely all of the time op? If asking him nicely to stop the noise isn’t working then you are allowed to stop what you are doing, look him in the eye, get down to his level and tell him very firmly to stop once. Use a low voice and body language to indicate disapproval. Then there needs be a consequence if he doesn’t such as a naughty step or something removed or whatever you have chosen. I think speaking to him very firmly and clearly once is worth a hundred of saying no constantly and too nicely! It just becomes a meaningless noise then. Choose your battles.
~as a pp has said, use humour where you can to help him make choices. Do you want to eat your toast like a bear or a rabbit?
Good luck op. He sounds like a fantastic little boy with great energy and imagination, and I can’t imagine how exhausted you must be, but it needs steering and directing eg if he keeps wittering on about the tigers, then again get down to his level and ask him to paint or draw the tigers, or model some with play dough, so you can understand more clearly? That way he feels heard but he is also occupied? Maybe?
Best of luck 🌺