Let \( x \) be the total time in minutes it will take to complete the video game.
Since you have completed \( \frac{1}{5} \) of the game in 23 minutes, we can set up the equation:
\[ \frac{1}{5}x = 23 \]
To solve for \( x \), multiply both sides by 5:
\[ x = 23 \times 5 \]
Calculating that:
\[ x = 115 \]
So, it will take 115 minutes to complete the game.