The average of five distinct integers is 110 and the smallest number among them is 100. The maximum possible value of the largest integer is

Sum of all the five integers = 110*5 = 550

The smallest integer is 100, so the sum of other four integers = 550-100 = 450

Now, for the maximum value of the largest integer, we need to minimise the value of other integers

The minimum value of other three integers can be 101,102,103 (as the integers have to be distinct)

So, the maximum possible value of largest integer = 450-(101+102+103)=450-306=144