The shift lever on the transmission is loose,

Regrettably, this is a common problem on the five speed transmissions. Usually, not only is the shift lever worn, but the shifter pawl shaft is usually worn as well. To replace either is a major job. To replace the shift lever, the outer and inner primary must be removed. To remove the inner, the starter must be removed and the primary chain, compensator sprocket, and clutch assembly.

If the shifter pawl shaft is worn, the guts must be pulled out of the transmission. It looks like the shifter pawl will come out without doing this but it won't.

Repairing this problem correctly is a major job.