How many times does 5 appear in all two-digit positive integers?

Two-digit numbers range from 10 to 99. Count of 5 in tens place: 50, 51, 52, 53, 54, 55, 56, 57, 58, 59 — that's 10 occurrences. Count of 5 in units place: 15, 25, 35, 45, 55, 65, 75, 85, 95 — that's 9 occurrences. Note that 55 has 5 appearing twice (once in tens, once in units), and both are counted separately. Total = 10 + 9 = 19.