Can a finger injury that happened five years ago still cause the finger to be bent and not straightened anymore? my right ring finger is still bent at the middle knuckle?

Yes, relatively common, injuries may result in healing with incomplete range of motion recovery due to multiple structures being possibly involved including nerves, vessels, tendons and ligaments, to name a few.

Yes. Can have persistent ligamentous contracture ,or boutonniere deformity that are chronic conditions. See a hand specialist for evaluation to see if this can be corrected.