Arrrrh, good old China Mobile is what I've been using (prepaid local Sim) for 5 years in HKG and CN - and 1st. time there with Motorola Q, had to visit their service counter & took tech support 10 to 15 minutes to mod the settings & get it to authenticate the HTC, only had Edge speed but it was good enough for Google Map, email & basic browsing, slow but usable all over town & in outlying countryside.

But, even if you're to pickup 3G/HSPA+ speed with the proper radio bands/hardware on the i5S, you would still likely get throttled to 2G - as that's the roaming partner agreements between the carriers. There's nothing we can do to "tweak" it and CMHK (sometimes shown as "Peoples" as the APN) isn't known for being fast, depending on the Sim card's preloaded/default settings - and in the old days, those supposingly're pushed & self-install by the carrier once it registered.

Travel frequently abroad, a good dual Sim smartphone like a new Samsung Galaxy Duo (4" screen) & factory unlocked on eBay/Amazon was going for around $120 USD shipped free would make a nice backup even without the latest 4G band, and the Moto G with the global GSM for under $200 wouldn't be a bad investment - pop in a local prepaid Sim & turn that into a WiFi hotspot, when T-Mo's free global data isn't fast enough.

(My current setup is a Nexus 7 with 4G-LTE and a Motorola Atrix 4G w. hi-cap battery (really HSPA+) and both run as a hotspot (thanks to customized XDA roms) when necessary as hotel chain's free WiFi are often useless.)