Personally, I don't think it is foolish to make the 5-hour drive if you have a good Plan B. And a good Plan B is, Cottonwood Pass walk in permits, climb Mt. Langley instead, if you get skunked on Whitney.
But if you compulsively check recreation.gov for a week or so before your entry, several times a day, you'll probably be able to reserve a permit for your desired day of entry.