Poor you, Flip, and poor little boy, too. I don't know your whole story, but will try and say something useful as another owner of a nearly-5 little boy.
I don't know anything about the SN end of things, but my ds, who has a very sunny and easy-going nature, good social skills and doing ok at school has also had tremendous rages over the past year or so, particularly straight after school. He comes out spoiling for a fight, and will keep pushing with the most ridiculous things until we're all shouting. At other times it just blows up out of the blue, and again lead to screaming tantrums from him and me biting my tongue to avoid joining in his tantrum (I don't always manage this...)
I've thought a lot about what's been going on and have come to the conclusion that being a four- or five-year old boy is incredibly difficult. There seems to be the whole hormone and peer-group thing going on that makes them want to rush around kicking and smashing things up on the one hand; but on the other, most of the little boys I know are also very sensitive and loving, and very thoughtful (often more so than my dd1 (8) and her friends).
I think the boys are really being pulled in two directions at once, and often find it incredibly difficult to hold it all together, particularly if there is any external stress going on (school, siblings, whatever). I've tried really hard to find a reliable solution that doesn't make it all worse -- it's very hard not to lose your temper when they're going out of their way to wind you up, but I found trying to remind myself that it was a sensory/emotional/intellectual overload and largely beyond his control helped (a bit).
The other thing that helped us a bit was to be very up front about the emotions involved, including how his behaviour affected us. So I often say: 'Are you trying to annoy dd1? I wouldn't do that, you'll just make her grumpy and horrible.' Or: 'If you shout at me, I'll end up yelling back, and we both hate it when that happens, don't we?' It doesn't always work, and you sound like a slightly crazed Joyce Grenfell, but it does sometimes help.
I found that confrontation, however tempting it is, just led to the kind of meltdown that you describe. I found it easier to deal with his unreasonableness if I reminded myself that it must be even worse for him to be at the mercy of all these powerful emotions that he doesn't understand. Sometimes when he's been hysterical on the floor I've said 'Poor you. It's horrible being so angry, isn't it?' Sometimes he'll let me pat him, sometimes not. If he won't, or he shouts 'Go away' or worse, I say 'All right, I'll come back in five minutes and make sure you're OK.' or 'If you need a cuddle, you can come down and find me.'
He seems to have a very powerful sense of pride, and the fear of losing face means that, although he needs cuddles, it's impossible to ask, or even to accept. This is hard to break through -- distraction sometimes works, as does humour, sometimes he just has to get over it by himself.
These are just random ramblings really, in the hope that you find something that might work for you. He is just a very small powerless little creature underneath all that anger, and it can't be an easy place to be for him either.
Hope things get better for you soon.