Calculate Remaining Height: 1/5 Daily Progress Over 3 Days

To solve this problem, we must calculate how much of the mountain Harry has not yet climbed after three days.

Let's break it down step-by-step:

• Step 1: Calculate the total amount of mountain climbed in three days.
  Harry climbs $\frac{1}{5}$ of the mountain each day. Therefore, in three days, he climbs:
  $\frac{1}{5} \times 3 = \frac{3}{5}$
• Step 2: Determine how much more Harry needs to climb.
  The whole mountain is represented by 1 (or $\frac{5}{5}$). To find out how much further Harry must climb, subtract the amount he has already climbed from the whole:
  $1 - \frac{3}{5} = \frac{5}{5} - \frac{3}{5} = \frac{2}{5}$

Therefore, the solution to the problem is that Harry must climb an additional $\frac{2}{5}$ of the mountain to reach the peak.