The motor buzzing but not running when you push the start button is a common sign that the motor is failed. It could be something is just holding it back (ie. something in the blower, etc.) but not usually. Replacement dryer motors usually run in the area of $100 and are not usually that difficult to replace.
There should be no reason that only a 5 year old dryer can not be repair economically. It sounds like the guy you talked to was just trying to sell you something. I assume he was a salesman and not a repairman?