Laura Turner and Laura Malarkey from the Mount School have explained how they worked out the answer to this problem:

n is equal to the number of tiles along one side.
We can calculate the number of edges in two different ways:
Method 1 - In total there are n² tiles on 4n² edges.
Method 2 - There are a total of 2n green edges which implies there are a total of 20n edges of all colours.

Therefore:
20n = 4n²
5n = n² (divide by 4)
5 = n (divide by n)

So there are 25 tiles in the set.