Answer

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**Hint:**We will use the concept of place values to write the greatest 5 digit number with 5 different digits. We will start from the leftmost digit of the number to the rightmost digit. For a number to be greatest among the other 5 digit numbers with different digits, we should have the highest place value for the leftmost digit. In a similar way, the rest of the digits should also have the highest place value at respective places in the number.

**Complete answer:**

We have to write a number that is the greatest 5 digit number and has 5 different digits. For the number to be the greatest, the leftmost digit should have the highest place value. It is a five digit number, so the left most place in the digit is the ten thousands place. The digit in this place with the highest place value is 9. So, the place value of 9 in the number will be 90,000.

Since all digits have to be different and no digit should be repeated, the rest of the digits in the number cannot have the digit 9. Next is the thousands place. The digit in this place with the highest place value will be 8, because we cannot use 9 and 8 is the second highest digit among the remaining digits. So, the place value of 88 in the number is 8,000.

Next, at the hundreds place, we will use the digit 7. So, the place value of 7 in the number is 700. Similarly, for the tens place, we will use the digit 6 and for the units place, we will put the digit 5. So, the number we get will be

$90,000+8,000+700+60+5=98,765$

Therefore, 98,765 is the greatest 5 digit number with 5 different digits.

**Note:**

The key concept in this question is that of the place values. We should be familiar with using the concept of place values for such types of questions. In this similar manner, we can write the lowest number with different digits. We can also find highest or lowest numbers in which we are given a particular digit with a certain place value and we have to find the rest of the digits to complete the number according to given conditions.

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