Is there a 5-regular graph of order 7? How can I decide  if there is  a 5-regular graph of order 7? 
Some hints or tips would be appreciated. This question arises in studying for a graph theory course.

It is not possible to have such a graph. More generally, it is not possible to have a $d$-regular graph on $n$ vertices for $d$ and $n$ odd. 
To see this recall (or convince yourself) that for $e$ the number of edges in a $d$-regular graph on $n$ vertices you have $2e=nd$.
