What does the above statement mean?

It can mean the set has 5 integers and all five are different..
Or
It can mean the set has any number of integers and only 5 are unique..

Yea, I know what you are thinking.. the first interpretation is the most likely & makes sense. However MGMAT seems to interpret in the second way when this statement occurs in a DS question. Sometimes MGMAT challenge questions seem that those are written deliberately ambiguously to lead the unsuspecting test taker to a wrong answer!

http://www.manhattangmat.com/ChallengeProblem.cfm?ID=112

Sets are not limited to one unique representation of each number; numbers can be repeated. The statement "Set S is composed of 5 different integers" does tell you that you have 5 unique values in there, but you don't know how many of each number you have. That interpretation is not unique to MGMAT - you will find the same interpretation on the GMAT because the information is only giving you only part of the mathematical picture.

For example:

{1,2,3,4,5}
and
{1,1,2,3,4,5,5,5}

both fit the description of Set S as given.