86 vt500 90/16

i am new to the darkside but am very interested. i have an 86 shadow vt500. rear tire is a harley dunlop 90/16. only have the 2 numbers. rim is about 4in wide and tire is about 5. i may be able to get a 6in wide tire in there but will be close. am a marine and will be upgrading to something a bit bigger in about a year after this next deployment. but for this bike does anyone know of a tire that would fit in there? i know it is a mighty thin tire and would be willing to lose overall height. speedo runs on front tire anyways.

thank you