It's definitely ambiguous, and all three readings you mentioned are possible. I would contact the vendor. But as I'm a computer scientist and native English speaker, below I've given my opinion on what the problem should have said for each equation you listed.
- "(1/5) * x", I would expect to read "The quotient of one-fifth and a number."
- "1/(5x)", I would expect to read exactly what the problem states, "The quotient of one and five times a number."
- "(1x)/(5x)", I would expect an even more ambiguous sentence: "The quotient of one times a number and five times a number."