I do my own oil changes and old Pilot used 5-20 oil and I have 12 quarts of 5-20 Mobil 1. My new to me 2015 Pilot will use 0-20 oil. I know I can use the 5-20 but what are the down sides to doing this?
Coming into summer I'd have no concern and plan to use 5 quarts of 5W20 I have leftover from my '06 Accord. I'd probably switch back to 0W20 back in the late fall/early winter when the first number matters.
If it really bugs you to have two different grades of oil send the 5W20 to me or you can mix the two grades preferably the same brand. Otherwise as mentioned thinner oil in the winter and slightly thicker in the summer.
I'm with the others..... while not "by the book", 5w-20 should be fine and probably even optimal for warm weather driving. My only reservations would be using it in very cold weather (under 20F) or if you still have remaining powertrain warranty in effect. (In the unlikely event you have a major oil-related engine failure, Honda will require you to show some evidence of appropriate oil changes for warranty coverage and I wouldn't want to give them any wiggle room to claim you used a "non-recommended" oil.)