A squirrel is climbing up a tree attempting to escape from a dog that is sitting $5$ feet from the base of the tree. The position of the squirrel at any time $t>0$ is represented by the equation $h(t)=\frac{t}{2}+3.$

At the moment the squirrel is $5$ feet from the ground, how fast is the angle of elevation from the dog to the squirrel changing?