Selection of at least two colours

Let there be three sketch pens of different colours. A regular pentagon is to be drawn using these colours where exactly one of the colours is used to draw a side and at least two colours are used to make the complete pentagon. In how many ways can this be done?

My attempt:

Each side can be drawn by using any of the three colours , so $3$ choices are available for each side. There are $5$ sides in total so they can be drawn in $3^{5}$ ways and the number of ways in which we can use only one colour is $3$ so the required number of ways $= 3^5 - 3$.

Did i miss anything?

$5$ sides and are given $3$ colors so we can take total no of functions which is $3^5$ required to use at least $2$ colors therefore we get $3^5 - 3$. We got everything required but the ans is not yet over because they mentioned it is a regular polygon which means it has all side identical that is $5$ sides are identical . Hence the correct answer is $\frac{3^5 - 3} 5$