Is it normal for a 5 month to do these things?

She sits up straight, pulls herself up in her crib, has tried standing up against the couch, and climbs into drawers.. Is this normal? She was a very big baby at birth, and seems to be developing faster than my friend's baby who is her age. Some people act like they don't believe me when I tell them how old she is. I think I would know.. Lol still, is this even close to normal?