0w20 and 5w20 difference isn't much during normal usage. 0w20 does force the oil to be a quality blend or full synthetic. Basically, in the aftermarket non-OE OTC 0w20's, you're forced to use a full synthetic as there are only a few 0w20's to choose from.
If you have full synthetic 5w20, feel free to thumb your nose at Honda and use it. Your engine won't notice unless you drive a flying sleigh and use parking spaces on the north or south pole.
I would NOT use a mineral 5w20 in place of a required blend or full synthetic 0w20, and is probably the only reason why 0w20 is a forced requirement. Cheapo consumers will do anything to save a buck and then blame the automaker down the road. This is one reason why 'options' aren't given by many automakers anymore.
Marketing dept's are still afraid of the words 'full synthetic'. So, they come up with weights or specs that require it and avoid those words. Sad that consumers buy vehicles from automakers that treat consumers like dummies.
Any engineer working for an automaker and can't give a VALID reason why a full synthetic 5w20 can't be used in place of a 0w20 isn't one that I would hire.
If you bought a new vehicle, feel free to change the oil whenever you want. Do it early. You're not going to save the world by using a few extra gallons off oil over the life of the vehicle. And, if you decide to keep the vehicle longer than what the automaker considers to be a 'life', MAINTAIN IT.