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.