What visa do I need for China if my fiance and I fly through Beijing and spend 5 ays there?

You need to apply for tourism visas. You should submit the following requirements to the related embassy or consulate, then they will process the visa for you in at most four working days:
1. Completed Visa Application Form (Form V2011A) with a passport photograph attached and supplementary Visa Application Form (Form V2011B).
2. passport with at least 6-month validity and at least 2 blank visa pages and one photocopy of its photo page.
3. If this is your first time to mainland China, you should provide copies of photo page of your current passport as well as other ID, e.g. previous passport, driver license, etc.
4. If you have been granted Chinese visa(s) before, copies of recent Chinese visa with entry record is required. If they are not on the current passport, copies of the previous passport with the above data are required.
5. You should provide valid Australian visa as well as entry record to the Consulate General (Original and the copy).

Please note that tourism visas are usually valid for three months from the issuing day. So you'd better go to apply for it one or two months before your departure date.