Your phone isn't capable of charging any faster than it's built to charge. The Nexus 5 had very limited support for Quick Charge 1.0 due to its processor, although my understanding is that this functionality wasn't enabled for the 5. But the phones are designed to pull only as much power as they can safely pull. If it can't take it, it'll negotiate a lower rate with the charger.
That said... 20-30 minutes to charge completely doesn't sound possible. I'm not aware of a single phone that can do that. So something's a little bit odd there...