Infant teacher here:
It's a difficult one. Some children just jump out at you pretty quick as you get to know them.
Key indicators for me as a Reception teacher that something MIGHT be a bit amiss in terms of ASD -
1: A robotic sounding voice. Rather monotone and "jumpy". "I.think.I.will.play.here."
2: Either uninterested in other children, or only interested when they are playing a game your child particularly likes. Generally plays alone but gets very involved in games.
3: Particularly interested in/good at computers.
4: Quirky physical mannerisms, eg: flapping their hands when excited.
5: Gets fixated on particular things. TV progs, films, toys, vehicles. Very keen to talk about these things to the exclusion of anything else.
ADHD is harder to identify because so much of it can put down to "normal 5 year old boy" behaviour.
However, if YOU are concerned, your doctor should take you seriously, and ask for a second opinion if you are not satisfied. After all, you know your child best, and if something in your gut says "something isn't right here", you're probably right. After all, it's SO hard and so sad to realise that something isn't all right with your baby.
I'd also speak to the school. Tell them your concerns and ask if they have noticed anything. They'll be very open and honest with you in these sorts of situations. Even if they haven't noticed anything in particular, the conversation will make them more aware of him, and they MAY start to notice certain things.