STS-5
The STS-5 crew wore the standard AB Emblem embroidered mission emblems on their flight suits and on their in-flight clothing, thus there is no rare 'crew patch' for this mission.
Embroidered Mission Patches
A-B Emblem patch
The AB Emblem patch was the version used by the crew.
Lion Brothers plastic backed patch
This version of the Lion Brothers STS-5 mission patch with a plastic coated back is the one most commonly seen. It is easily recognized by the wrap-around pale blue windscreen on the Shuttle plus the fact that there is no flag on the Shuttle's wing.
Swissartex patch
The vintage version of the Swissartex STS-5 mission patch exists both with a waxy plastic backing and with a vacuum sealed clear plastic coating on the reverse. The fronts of the two versions are virtually identical.
Cape Kennedy Medals patch
This plastic backed patch was most likely made by Cape Kennedy Medals. The fine details on the tail are quite distinctive, with pale blue shading in the center and a white leading edge and rudder.
Lion Brothers bare back patch
This version of the STS-5 Lion Brothers patch with a bare cloth back is extremely rare. Like the more common version it lacks a flag on the Shuttle's wing but it doesn't have the same wrap-around windscreen.
Footnotes
[1] Example sales of STS-5 Lion Brothers bare cloth back patches:
eBay item no. 181002779785 Oct 25, 2012, sold at $100