Number of edges in a planar graph where every face has five sides

Question

This was a practice question I saw.

I'm kinda confused about the part that says $5f = 2e$. Could someone explain that?

Question: What is the number of edges in a planar graph where every face has five sides? (Answer in terms of $ v $, the number of vertices.)

Answer: $ \frac { 5 ( v - 2 ) } 3 $. Eulers $ v + f = e + 2 $. $ 5 f = 2 e $ by counting edge face adjacencies. This implies $ v + \frac { 2 e } 5 = e + 2 $, which implies $ e = \frac { 5 ( v - 2 ) } 3 $. Notice this puts conditions on the values of $ v $ for which this can hold.

Answer 1

Double count the edges: Each face has $5$ edges ($5f$) & each edge is an edge of exactly two faces($2e$) (because the graph is planar.)