Will I have trouble with my luggage - Transit through Beijing Capital Airport PEK I->I

Good day,

My itinerary are as follows: AKL -> (Air China) PEK -> (Uzbekistan Airways) TAS
I am NOT a holder of a passport from the listed 45 countries (I have an Uzbekistan passport) and hence I do not qualify for the 72 hours, hence I will go in under the 24 hour free transit visa rules.
It seems like there is no relationship between Air China and Uzbek Airways, hence I may have to collect and re-check my luggage in PEK. Will I have any difficulty exiting and re-entering the transit zone to do this? Am I not able to transfer my luggage to the final destination through the transit area?
And are there any other possible difficulties I will face based on this itinerary i.e. different terminal locations? (The stopover time is 5 hours, hence I should have no problems rechecking my luggage if applicable).

Thank you in advance :)