General aviation pilot reported a collision with a UAS while in cruise. The pilot landed as a precaution and found damage to the aircraft.

Narrative

On the morning of Day 0 I departed ZZZ in Aircraft X. At approximately XA:37 (based on flight tracking) I struck a drone approximately 13 NM NE of ZZZ. I was northbound climbing through 5;500 ft. MSL (3;500 ft. AGL) at approximately 80 kts. I felt something hit and heard a bang; and saw something large and dark (seemed roughly basketball-sized) go past me in a blur on my left and strike the left wing just outboard of the pitot tube and continue on over the top of the wing. It happened so quickly that I thought the impact jolt and noise were caused by the wing strike. After verifying that the aircraft was still flying well and fully controllable I returned to ZZZ to check for any additional damage. After landing I discovered a shallow dent in the left wing leading edge at the location that I saw the object strike the wing. I also found that the prop spinner had been torn off of its mounting bracket; and the prop blades were damaged. One propeller blade had large sections near the tip where the epoxy paint coating had been abraded down to bare metal; and gouge damage to the leading edge. This blade was bent and had to be straightened by the repair shop. The other blade showed less contact; but does have paint/plastic witness marks. Note that this prop was installed new and had no prior damage or marks. There was also a dent in the front of the engine cowling; with the impact force causing a cowl latch to shear off. I feel I was very lucky to escape this occurrence without suffering worse damage that would have lead to a crash.I believe that mandatory strobe lights should be required on all drones to give pilots some small chance of seeing and avoiding them; especially when they are being flown far above their legal ceiling. Harsh penalties similar to laser pointer use should be applied to illegal operations as well. And finally; I reported this to the authorities but never received a call back. I would very much like to see a drone midair at 3;500 ft. AGL taken more seriously by those in charge of our safety.