Here's a comparison of them.
http://www.gigabyte.us/products/comparison/list.aspx?ck=2&pids=5832,5489
The gaming 5 has slightly better audio, newer codecs and additional audio amplifier, it also has usb 3.1 type c and type a, the d3h doesn't have those. You can crossfire on the d3h but not sli, the gaming 5 supports both crossfire and sli. It depends on whether or not you want those features, a more feature rich board costs a bit more.