Ignoramus9483 wrote:
My son is 8 years old and surprised me recently. He could not run all
the way up to a 30 foot tall (in my estimation) hill.

I am 38, moderately overweight, and I have not exercised much in a few
years due to so called "lack of time". And yet I could run all the way
up that hill with a 40 lb toddler in my arms, and he could not even
run up without stopping. My 8 year old son is not fat, in fact he is
skinny.

Another time he ran up 5 stories of a apartment building and again
could not run all the way, and had to breathe very heavily afterwards.

Would I be justified in being concerned, e.g. should we talk to a
doctor, or is it within some normal bounds that can be corrected with
exercise?

Yes, I would be concerned. My 8.5 year old has no trouble with that kind of
exertion and more and I woulld put him just over average in fitness and
stamina for his age. He runs rings around me. Does your son spend all
lunchtime at school in physical activity? Does he ride his bike or scooter
regularly? What sports does he play? Does he swim laps yet? (My son can swim
50m freestyle but does pause a couple of times during the lap because his
breating isn't correct yet.)