Your SR has a smaller diameter carb than the regular KDX250, so you need a #6 slide for your carb, and not a #6 slide for a regular KDX250.
The #5 and #6 refer to the millimeters of cutaway at the bottom. You can see this in your 2nd photo, where your stock SR #5 slide clearly has less cutaway than the #6 KDX250. More cutaway on the slide will absoltutely make the bike run leaner at low and mid rpm, and can really benefit some bikes.
Hopefully JD can get you the slide you want. Make sure they know your bike is the SR, and tell them the model and diameter of your carb.
As an alternative, it is possible to grind away 1mm of cutaway from your stock slide opening to make a homebuilt #6. Scribe a line and work up to it with a dremel. Of course, there is no turning back once you remove material.