That means the clutch is dragging then, not slipping. If it was slipping it wouldn't have full engagement.
You can try to adjust the cable on the handlebars, or you might have to adjust the rod on the basket inside of the clutch cover.
EDIT: I re-read what you're saying and you say it drags a bit. Does it revs up easily(while riding in gear), or is it hard to shift because the clutch isnt disengaging?
If it is infact slipping in higher gears it's probably time to get a new clutch set as yours is worn out.
You worded it semi-confusing lol