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 $n ²$ tiles on $4n ²$ edges.
Method 2 - There are a total of $2n$ green edges which implies there are a total of $20n$ edges of all colours.
$20n = 4n ²$
$5n = n ²$ (divide by $4$)
$5 = n$ (divide by $n$)
So there are $25$ tiles in the set.