A) Lodestone says your only combat class is Pugilist.
B) "5th slot from the left" on SCH would be your level 50 slot, which is impossible to have at level 34.

Something is inconstant here.

In any case. Classes (Arcanist) get cross-class slots every 5 levels (6 at 30, 7 at 35, 8 at 40, 9 45, 10 50) where jobs are every 10 (3 at 30, 4 at 40, 5 at 50).