OK I' ll try my wisdom on this one. This deer was walking. If he was trotting, the tracks would be in a straight line slightly off center of each other. Second, the left print is the deer' s back hoof print and the right track is the front hoof print. Deer have a cerain stride and when they walk, the rear feet are placed in almost the exact spot vacated by the front foot. With younger deer, the hind feet sometimes overshoots the front feet. (prints) With heavier deer, they seem to have a shorter gate. Sooo, the front foot print (specifically the tips of the toes) will appear in the front of the rear hoof print. (like in your picture) The front hooves are usually larger than the rear ones. On hard ground the deer walk on their tips since the hoof slopes up in the back. When the ground is wet or muddy, the entire hoof is used and the dew claws come into play.
7" long and 5" wide is an elk! On a 150 pound buck, the overall front hoof length including dew claws is about 4 1/2 inches long by 2 3/8 inches wide. (This is from one of my favorite books and the the author says the tracks were measured in soft muddy ground.)
So in my estimation, this was a deer that stepped in the mud. It was about averge in size, and oh yeah, it was heading that way over there.
Greg