In my neighborhood, Belgrano, there are a lot of good places to get bikes for kids. There's one on Monroe called Green Line, I think it's between Cuba and Vuelta de Obligado and another one on the block before, Cuba and Arcos. I might be off by a block but not more than that.
What surprised me is that kid's bikes are almost as expensive as adult bikes--I don't think that's the case in the states, but I could be wrong.
If the 5 year old is a girl, I may be able to help you with a used bike. Not to perpetuate gender stereotypes or anything--your hyothetical son is as equally welcome to a pink, white and purple bike as your daughter, but my son began refusing to use anything pink after turning four (and moving to Buenos Aires, where boys who like pink are not as tolerated as they are in San Francisco).