If the PCs want to sit around for 20 minutes, why would you want to stop them? How does it make the game more fun to limit the use of healing powers between combats? This rule smells like railroading and I don't like it.
If the PCs are in an obviously dangerous or urgent situation, they shouldn't be resting at all. But saying that a 5 minute rest is fine, while a 15 minute rest has a substantial chance of attracting a monster, seems like you are forcing your players to do something they don't want to do. Obviously, if your players are OK with this rule, then go for it, but if I were one of your players, this rule would really annoy me.
-- 77IM