Xi'an, Luoyang Grottoes, Shaolin Temple, Zhengzhou

If you wanna have a god visit, I suggest you omit the temple. Then your time can be ok to arrive at Zhengzhou in time. The bullet train from Xian to the Grottoes takes no more than 2h, and the train to Zhengzhou takes only about 40min. But if you really wanna enjoy the temple, I'd suggest you hire a car for a round trip to save time, then your timing still can be fine.