\(500\) is a three digit number so possible numbers below \(500\) can be \(1\) digit, \(2\) digit, and \(3\) digit numbers above \(100\) and less than \(500\)

However not all the numbers are included only those numbers that are formed by use of \(1,2,3\) and \(5\)

Three digit numbers:

There are three places for three digit numbers Hundreds, tens and unit so

for the hundreds place except \(5\) all given number can be placed so there are \(3\) possibilities

for the tens place there are \(4\) possibilities and

for ones place there are \(4\) possibilities too

in total \(3*4*4 = 48\)

For \(2\) digits:

there are \(4\) possibilities for tens place and \(4\) possibilities for units place

therefore, \(4*4 = 16\)

For \(1\) digit there is \(4\) possibility

Therefore total possibility = \(48+ 16 + 4 = 68\)

option D

_________________

This is my response to the question and may be incorrect. Feel free to rectify any mistakes