I'm not exactly sure if I'm right but I wanted to double check on how I approached this problem. If its wrong, can you please provide me with hints or suggestions or maybe an answer which an explanation?
So since there are 12 * 5 = 60 / 2 = 30 edges? b) degrees would be 5-1 * 30 = 120 degrees? I think I'm completely off but please help
The sum of the degrees of the vertices of $G$ equals twice the number of edges. This follows by double-counting the pairs $(x,e)$ where $x$ is a vertex and $e$ is an edge having $x$ as one of its endpoints. Counting over vertices, there are $\sum_x d(x)$ such pairs as there are $d(x)$ such pairs having $x$ as a vertex (here $d(x)$ denotes the degree of $x$). Counting over edges, there are $2m$ such pairs since there are $2$ such pairs for each edge, $m$ being the number of edges. It follows that $\sum_x d(x) = 2m$.
For a) your answer is correct. For b), in a $k$-regular graph with $p$ vertices the sum of the degrees equals $kp$, hence there are $kp/2$ edges (which shows there are no regular graphs having an odd number of vertices where each vertex has odd degree).
