here are no cars outside alaska in the winter that need 5-10 oil it is way too thin for normal use , you need 10-40 for most of mainland america thinner oil like 5-30 or 5-20 is only used in new cars to meet federal mileage regulations in artificial conditions on a rolling road , real world conditions need a heavier oil

We need the make, model, year and miles on the car. What is the spec oil and why not just use that?

5w10 is very light, so maybe you are getting some sludge or deposit being burned off.

Black smoke or white?

pull the smok out of the tail pipe and go back to 10-30

Harley Drive is right. Also, different brands of oil react differently in high mileage conditions.

always , always follow rule number 1 ---- use the manufacturers recommended oil grade .

rule number 2 dont sway away from rule number one.

piston rings, valve stem seals or a failed pcv valve are the ideas that ceme to mind.

Yes, of course.