Make the greatest and the smallest 5 - digit numbers using different digits in which 5 appears at ten’s place.

Here, the ten’s place is fixed( = 5).

For the rest of the digits; Let’s use the digits in this way:

To minimize the number, the smaller digits will be used in left side;

And, to maximize the number, larger digits are used in left side. [As the left side digits contributes more towards the value of the number: Any number, say, ”a_na_{n - 1}a_{n - 2….}a₁a₀ can be expanded as :

= a_n × 10ⁿ + a_{n - 1} × 10^{n - 1} + a_{n - 2} × 10^{n - 2} + a_{n - 3} × 10^{n - 3} + … + a₁ × 10¹ + a₀]

The greatest number = 99959

The smallest number = 10050

[note, as we can not start a number with 0, we are taking the 2^nd smallest digit available (here, 1) to start with while forming the least number.]