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