Vintage Slingerland shells would be thin 3-ply shells with solid maple reinforcing rings at the bearing edges. The interiors would either be mahogany (pre-1963) or maple (post-1963). Drums produced in the late 1960s would have a "chocolate milk" colored interior stain.
Your bass drum doesn't appear to be a 3-ply shell, nor does it have reinforcing rings. It has a grey interior, which Slingerland never used. It has metal hoops, which wouldn't be original on a vintage Slingerland kit. The bass claws and t's aren't the right shape. The spurs aren't right, and neither is the consolette. The mounted tom's depth looks too shallow. The toms and snare have triple-flanged hoops with an outward flange instead of Slingerland stick savers.
As for the snare... The pictured snare isn't a Ludwig. Did you receive a different snare?
Did you get the drums, hardware, and cymbals for $500? If so, you still might've done well. At least some of those cymbals look like nice Avedis Zildjians.