This house was built in 1957. Tub measures 57" long by 30" wide. I was thing
It is a standard 5 foot tub. Maybe the tub is recessed into the wall about 3" so
the overall length is 60" Is that possible?

Yup! They make 4 foot tubs, 4'6" tubs and 5 foot tubs, so most likely, you have a 60" tub recessed in the 3" as you thought!

If you open things up and find differently, please do let me know, OK?

Mark