How many two digit number contain no 5?

Answer 1

There is a possible confusion over how the last part of your question ("contain no 5") can be interpreted:

1. it could be a badly written shorthand of the word number: "Nº" also written "No." also written "No" and very badly written as "no", meaning "contains the number 5", meaning "the number 5" - the number between 4 and 6 and less than 10;
2. it could be a badly written shorthand of the word number: "Nº" also written "No." also written "No" and very badly written as "no", meaning "contains the number 5", meaning "the digit 5" - the digit 5 in any place value column;
3. It negates the sense so that "contain no 5" means "do not contain the digit 5".

In interpretation number 1 there are no such numbers, as 5 is less than 10 and all two digit numbers are greater than, or equal to 10 (I suspect that this meaning is definitely not intended).

There are 90 two digit numbers (10 - 99); of them:

9 contain a 5 as the second digit: 15, 25, ..., 95

10 contain a 5 as the first digit: 50, 51, ..., 59

So there are 19 of the digit 5 used.

However, 55 is counted twice, meaning there are 18 numbers which contain the digit 5. (This is the solution to the interpretation number 2.)

Which means there are 90 - 18 = 72 numbers which do not contain the digit 5. (The solution to interpretation number 3, which I suspect is the required answer.)

Use whichever solution meets your intended interpretation of the question you wrote.

Answer 2

There are 19 such numbers.