Hammering home the challenge that Apple faces in China with the iPhone is a report that only five units have been sold during the first two weeks on the official carrier’s online store.

China Unicom opened an official iPhone store in mid-November on Taobao.com, the largest Chinese e-commerce website, according to PC World. Similar to eBay, the official store has thus far sold only two 8 GB iPhones and three 16 GB iPhones, if figures on the site are to be believed.

Taobao is China’s top online retail site, where many users go to buy items like mobile phones and laptops. China Unicom is also selling the iPhone through its own website, but no sales figures are listed there.

The official iPhones from China Unicom have to compete with unlocked units brought in from overseas, which many users purchased well before the official deal with Apple was in place. Apple was forced to remove Wi-Fi from the devices before China Unicom could sell them officially to comply with local regulations (which have since been removed, ironically). The final hurdle for the iPhone in China is the steep price: 6,999 yuan ($1,024 US) for a 32 GB iPhone 3GS with no service, compared to $800 in nearby Hong Kong.

Previous reports pegged the early China Unicom sales at around 5,000 units in the first few days after launch, which looks particularly bad when compared to last week’s South Korean launch where carrier KT racked up 60,000 online orders for the device.

Last month, a China Unicom executive was openly optimistic about the iPhone’s chances in his country, predicting 10% of China’s 3G users to buy the handset, according to Chinese state media.