Here are their names:

KAMBOULE Wingnaana Beatrice (athletics)
OUEDRAOGO Mamadou (swimming)
OUEDRAOGO Palingwende Levy Nathanie (athletics)
SANON Olivier (athletics)
SANOU Idrissa (athletics)

Good luck to them all!

All five of Burkina Faso's athletes are in Athens because of Olympic Solidarity scholarships. A nice quotation which justifies this funding:

A veritable abyss separates the high performance athlete receiving a gold medal on the podium from the athlete cheered on by a child in a small courtyard or amidst the desert sands. Nonetheless, our ideal is the same: it should be possible for everyone, in spite of very difficult beginnings, to have an equal chance when facing the standards of high level international competition, even though, naturally, only a small fraction will get to stand on the Olympic podium.
Lord Killanin, 1979 – Président du CIO de 1972 à 1980.

Find out more about the Burkina Faso Olympic team on the Athens 2004 website.