My database of jazz discs says I'm about 7.500 discs, with several remarks:
a) it also includes mp3 (the recount can only be done by item, not by format)
b) multiple box-sets are counted by the number of individual discs (this is, a 5-disc box-set contributes with 5 discs)
c) discs with more than one leader are duplicated (this is, a Gonsalves-Terry leaded disc is included as one disc by Gonsalves and one by Terry).
Classical, flamenco, rock and pop discs are stored in my attic and are part of a different database.