Depends. I used to live in Los Angeles. 5,000 miles in the city is significantly more engine hours vs 10,000 miles on uncluttered freeways of metro Cleveland where I live now. So in LA I changed synthetic every 5-6k. Here in metro Cleveland, currently I have semi synthetic and will change it tomorrow at roughly 5,500 miles on it. I'll fill a conventional and will do a change at 5-5,500 mi. If I'd still lived in Los Angeles, I'd plan on a ~3k interval. Now that's on my 29 year old car.
With lease vehicles I follow their oil life monitor and do a change between the remaining 5 and 10%. I usually stick to the recommend grade, unless owner's manual specs a heavier weight for the rest of the world, then I'll use that one. For example: I had a 2014 Mazda 6. US spec was 0w20, but rest of the world speced 5w30, so I used that