Since it's only a 5" disk, it could very well use a shaft smaller than 5/8".
I have one of the smaller disks that use a 1/2", and yet another that uses 3/8".
You're gonna have to measure and find out what you need.
Regarding the shaft, try to keep it short. The shorter it is, the less likely you have a circumstance of slight bend in the shaft, which contributes to wobble.
Also, if you can, try to obtain an actual shaft rather than a simple piece of "round stock". It costs only slightly more, but the benefits are great. The material preferred for shafts is turned and precision ground to tight tolerances, then polished. What this equates to is a
tight fit in the hub (which is what you want). Also, this type of material has always come to me straight, even in the 36" lengths.
Here is a link if you need sourcing:
http://www.speedymetals.com/c-8240-turned-grnd-polished.aspx
This particular supplier will do mail order, and they have no minimum. I do not include the link to direct you there as a customer, but merely to specify the type of material best suited for this application.
Good Luck,
Rob