Do you have 1st gear (down 1 from neutral)?
Either way:
Get the e-copy of the service manual and study clutch fiber replacement and cable replacement. Then read around here for tips and tricks.
Then disassemble the entire clutch and basket and take pictures at each step. Notice the Disc wire and other bits that can be removed in favor of all full Disc linings (no half linings).
Re-check your motor oil for metal. If none then read-up on the transmission gears and dogs. Learn how the (push) aka (pull) lever works. Learn about the motor-end cable connection angle. Also learn how to set-up the handlebar clutch lever.
If you don't find or stumble-across the solution then your transmission needs to be disassembled, which means splitting the cases.
From what you have posted, it seems unlikely that a prior owner was clutchless 'speed-shifting' and wore (for example) the second gear tooth height, because you would notice having to shift again. So your 5th gear might be missing. But it doesn't make sense either.
The devil will in this case be in your details.