5hrs at Beijing capitol, terminal change

hello,
I'll be arriving in Beijing on a regular tourist visa, staying there for two days and then leaving for Korea for a few days. Afterwards I'm traveling from Korea to Singapore via Beijing, but I will have to collect my luggage in Beijing, change the terminal (arrive at T2, depart T3) and recheck my bags with another airline. I have about 5 hrs between arrival and departure.
Should I apply for a multiple entry type or can I use the 72hr transit option, or is there an entirely different option available?
Thank you!