I think that you are correct. The answer is 30.

However, that depends on the fact that the two colourings that I have shown are counted as different. I am not at all sure that there are different.

That figure is known in graph theory as an unlabeled graph.

The second figure that I give is a labeled graph and in that case the two colourings are clearly different. This graph is known as a bipartite graph. We can be partitioned into two set of vertices: {A,C} & {B,D,E}. There is no edge between any two vertices is the same cell. There are 3 ways to colour A & C the same colour. Hence there are ways to colour B, D, & E some other colour. That gives us 24 ways. But there are 6 ways to colour A & C with different colours leaving only one way to colour B, D, & E: a total of 30 for the labeled graph.

I would argue that the question is not clear on the point.

POST SCRIPT.

I have just proved that there are only 24 ways to colour an unlabeled graph.

That is not one of the answers. So we must conclude that the question is about a labeled graph.