Not sure as I've only used the airport at the end/beginning of itineraries; however, I can say the airport is pretty straightforward. Its small and the two times I've used it, the flight I landed/departed on was the only scheduled flight for that time of day. I'm assuming your flying in on Turkish and out with Air China? If so that's the same route I took (FRU-ULN, ULN-PEK).

When I landed I was in J and was able to pass through customs fairly quick (5 minutes tops). The longest part was waiting for my bag (a good 30-40 minutes). When I departed lines were fairly quick as a foreigner (American) and I was able to reach my gate within 15 minutes.

If you have priority pass there's a lounge after customs where all the souvenir shops are. Don't mistake the pre-security/landside lounge for the priority pass one, two different ones. I was the only one in the lounge which meant more beer and snacks for me

FYI I did this last January and because of the weather, the flight was delayed in landing by an hour (we circled above the airport, I', assuming because the clouds/smog was so thick.)

Are you planning on staying in the airport or visiting the city? With 5 hours I think you MIGHT be okay going into the city for a quick lunch, that is if your willing to spend the money on a taxi there and back. Public transportation will more than likely be to slow. If you go outside just be careful with patches of ice on the ground, I slipped more than a few times walking the streets.