After thinking about this I think that you have a compressor that is older than 25 yrs if you need to add oil to the motor bearings. So take the below with a grain of salt.
The Sears compressor I have I run Amsoil Synthetic Compressor Oil - ISO 46, SAE 20.
I think I bought it about 1993 5hp 30 gallon tank. I had a 5hp 20 gallon one before I sold to a friend. The motor and compressor were exactly the same.
Since my first one is close to the age of yours. I think that you probably take: Compressor Oil - ISO 46, SAE 20. Whether you use syn oil or not is up to you......
Probably anything you find in a store that sells compressors has this viscosity I would think. Sears would be a slam dunk, I think they even have conventional and synthetic oil? If so take your pick.