If don't want to use algebra, just logical thinking...

1. The sum of $5 notes needs to end in 0 (not in 5), because the sum of $2 notes can't be end in impair number. => we have even-numbered $5 notes => we have even-numbered $2 notes.
2. possible variations for a $5 notes (to make it less than 50):
   A. 2 pieces: $10
   B. 4 pieces: $20
   C. 6 pieces: $30
   D. 8 pieces: $40
   E. 10 pieces: $50
3. Based on the 2nd point => the sum of $2 notes need to end also in 0. => the possible variations:
   a. 5 pieces: $10
   b. 10 pieces:$20
   c. 15 pieces: $30
   d. 20 pieces: $40
   e. 25 pieces: $50

For a total amount of $50, we need:

• A,d
• B, c
• C, b
• D, a
• E
• e
  Of the above 6 options, only in one case is the total number of banknotes 16 (C, b)

The answer: Harry have 6 pieces of $5 notes.