"Wooden spoon" has a special meaning celebrating an individual or team which has come last in a competition (but sometimes also runners-up). An actual wooden spoon may be humorously awarded, but even if there is no physical trophy, the phrase "winning the wooden spoon" may be used to mean coming in last place.
It's not grammatically incorrect, but to my native ear, it sounds a little weird. It would be much more natural to say, "The fifth spoon is made of wood." However, you might hear something like, "Our sheets are of the finest satin." I think it sounds less weird if you say, "... are of the finest satin," rather than simply "... are of satin."