Of course, there are several sleeping trains from Beijing to Xi'an. Child is also OK to take a train. So, please, consult your hotel in Bejing about that and they will help you to book train tickets. If you are going to Xi'an from Beijing air port directly, I suggest you to go to Xi'an by air.

Hi, there are both train and flight to xian. The train to xian starts from beijing west railway station. It will take about 11 hour by taking the fastest train. The cost is about 400 yuan for a soft sleeper.
If you want to travel by plane, it only needs two or three hours. If you book the ticket early from the travel agency, you can get a big discount. the price is about 500 yuan if your book one month earlier.
I think you'd better take a plane and book the tickets in advance, which is faster and more comfortable.

Hi, we travelled from Beijing to Xian by train when we were in China earlier this year with our 3 year old son....highly recommend the train trip as it is overnight, so you dont lose any sightseeing time. Fares for children go by height, so if your 5 year old is under 1.4m (I think) and can share a berth with one of his/her parents, he/she will travel for free. Trains leaves Beijing approx 8:00pm and arrives Xian at about 7:30 to 8:00am. Hope this is some help to you.