"It’s just one." -- confirmed by Jeffrey Bellinger, designer of Killer Bunnies, in an email reply.
This is an interesting case where a revision of a card's instructions made it much less clear. The original description read:
May be used once by a player to retrieve and immediately use any Run card from the top seven cards of the discard pile.
In a later series the OP draws their description from (the wiki speculates ZZ series), the description is revised to:
May be used once by a player to retrieve and immediately use any of the last five Run cards played.
I find myself personally convinced by @GendoIkari's arguments, specifically based on the phrasing "any Run card" in the original description. This interpretation is also helped by the phrase "used once". Unfortunately, both descriptions are truly ambiguous. If my interpretation of the card's description is correct, this ambiguity could have been resolved by using the phrasing "any one" instead of "any". On the other hand, if it was actually intended that you to take all five (or up to seven) cards, the card description could have said something along the lines of "May be used once by a player to retrieve and immediately use or rediscard all of the last five Run cards played."
@Benjamin Cosman's argument is also compelling. It does seem overpowered to be able to play 5 (or potentially up to 7) cards: imagine retrieving multiple Choose a Carrot cards. However, using multiple run cards in a turn is not without precedent: W Is For Whammy allows you to launch all 5 weapons, but Retrieval's expanded form could be significantly more powerful than the sporadic 5-card hand nature of Whammy. Though one never can tell what "balanced" really means for a game like Killer Bunnies... EDIT: Turns out you were pretty spot-on in your analysis; Bellinger said it would be "[T]oo powerful that way!"
@BJ Myers point about how the phrase "any number of cards" would have been used if multiple draws were intended may be true, but I'm not sure how often I've seen that specific phrase in Killer Bunnies. I think most cards' effects are scoped, so they would be more likely to phrase it using "all" like "all Weapon cards in his five-card hand" (from "W is for Whammy"). The underlying point is the same, though.