It definitely seems to be hit-and-miss when it comes to finding 5/8" at HD and Lowe's.
It's a little late since the discussion has gone off. But...
You can reduce your search a bit at Home Depot.
Go to your Special Services Department at home Depot. The name has probably changed to Special Orders, Customer Orders or Customer Services. The lumber desk might have employees that know how to do this, but I wouldn't bank on it.
If you find they don't have 5/8 sheets in the actual store. Ask the desk to do a store search for the 5/8 sheets. This might entail actually having a SKU (a six digit number attached to all product in the form of ###-###). All Home Depots have the ability to look up other stores inventory. By default, the search algorithm can search inventory of six or so of the nearest stores. But you can search specific stores within the region (I never tried searching outside the region) by putting in the store number.
If they tell you they can't look up another stores inventory, they're full of ---Cleveland steamer---. As long as you have the SKU and know the store number within the region you want to search, it can be done. Call a manager at that point.
If they tell you it's a special order item only, that's partly true. But they're still full of ---Cleveland steamer---. The store I used to work at 5/8 anything was special order, but the Home Depot across the highway (a ten minute drive) carried an entire inventory of 5/8 boards. They just want to get the extra money for their sales quota.
Bear in mind that the inventory count between stores isn't updated live. Worst case scenario is that stock numbers were as of midnight. Best case, counts were two or three hours old. But I have serious doubts there's such a huge demand on 5/8 boards that that would be a huge issue.
90% of the people you encounter won't know how to do that kind of search or won't want to do that kind of search.
Lowes has the same ability, but I don't know the extent of their search routine.