GoldPremier -
Probably the biggest limitation you're going to face is the fact that there are 5 of you. Assuming that there are two couples + 1 extra, you would need a 3 bedroom apartment, since most of the rentals have one queen/king bed per bedroom. The other possibility is to rent two apartments in the same building - for example in my building in Las Canitas, one of my neighbors has two side-by-side, 2 bedroom apartments as rentals.
If you go to
www.apartmentsba.com (as an example, I have no connection with them), you can search based on barrio and number of persons, to get an idea of what is available and pricing. Many of the high-end apartments for rent are specifically directed towards US/European tourists (and are often owned by Americans).
Take a note of the size of the apartments (photographs can be deceiving), and what amenities are available (for example if you intend to rent over the summer, air conditioning is a necessity).
It's difficult to make a recommendation as to what barrio without knowing more about your expectations. Most will recommend Recoleta as a "safe bet", but personally I'd rather be in Palermo ...
John