The largest 5-digit number having three different digits is

To obtain the largest 5 digit number, digits must be used from 9 in the descending order.

As we have to use 3 different digits, they are 9, 8 and 7

Also since we need the largest digit, only the ones and tens place be filled by 8 and 7.

Rest by 9 which is the largest digit.

Hence, the answer is 99987