The included items and timing of the promotion seem to be in response to Wendy's 4 for $4 deal introduced last winter. Like the Wendy's deal, you get about $5 worth of food for $4, although the cookie from Burger King means you're also covered for dessert.
McDonald's has also recently thrown its hat into the mix with the new McPick 2 menu.
The 5 for $4 deal is available at participating Burger King restaurants for a limited time.