I have the same problem with my 630. The serial number tag is on the left side panel just like your 530. Over the years these panels are removed and never replaced as they are non functional. Your serial number and mine are probably either sitting on this panelin the corner of a shed somewhere or thrown out behind that shed to rust.
The engine block number has nothing to do with the actual tractor number ubfortunately and unlike the older VA, S, D, and LA tractors the tractor serial number is not stamped on the engine to transmission flange.