IPSEA
SOSSEN
The School Exclusion Project.
Those are all charities.
If they can afford it, ADHD assessment should be the 1st port of call (private, sadly) as meds can be life changing for those who have it.
these people are clinically great, and relatively affordable (as affordable as complex needs healthcare gets).
Second on the list is medico-legal assessment and a lawyer, as EHCP provision can vary wildly by LA and by case. The law is clear but funding is such that the only kids who get what they are meant to are those with parents willing and able to force it.
A barrister called Alice de Coverley used to head up the School Exclusion Project and now represents kids who have complex needs through the EHCP process. She can recommend specialists to assess to ensure any EHCP is fit for purpose, and she is amazingly effective herself. She's kind and capable and normal as well as brilliant in legal terms, and she's genuinely passionate about children's rights. She's very busy but her Chambers have other excellent barristers (and direct access barristers are much, much cheaper than solicitors) so if she can't help she can steer your relatives to someone who can.
It's not screen time. It's not parenting, not unless there are huge traumas in the child's past you are unaware of. Everything you describe is common with unmet needs in neurodiverse kids, right down to the late toileting, impulsivity, outbursts of anger. And with the right help, children can thrive.
If he has sensory needs then the setting you describe is horrendous for him, too. That creates the 'fizzy pop' reaction, where a kid just can't contain it and explodes. Sensory assessment by a good OT can establish that, and he needs a specialist speech and language assessment, too, to work out if he has major barriers in communication that can be missed (especially in a more able child).
He's only five, there's lots that can be done. But unfortunately time matters.
My eldest, and I had the ASD assessment done first, too. He got the diagnosis, and sod all else. A few years later we had an ed psych, OT and SLT assessment and huge needs were found - he now has the support. My second child, and we went for the ADHD assessment, and then she was medicated and it helped enormously - but the autism came through far more as a result. I didn't go with that assessment, from experience: I had the OT and SLT ones, and started the EHCP process based on them. The autism assessment was done as part of the EHCP statutory assessment process, and she was diagnosed then.
If I had known all I do now at the start, my son's path would have been very different. Your relatives need to lock into the parent support network - search out Facebook pages etc for parents of kids with additional needs. It's a hidden world, but everything I have for them now, including the details of the above specialists, came from other parents.
I send love to them, and I'm glad you care so much. Sadly, they will have many years ahead of people assuming it's parenting. Not infrequently teachers. I wish I'd had the assessments done earlier, and not assumed it was me and diligently done the courses, which just delayed his proper assessment and therefore his support. You can't support needs you don't know are there. With my second, I was on it at once and she has had help from very early on. It's been a game changer.