Please help. Doesn't less than -3 mean smaller as in going further into the negatives?

If a number were less than -3, the only possible choice is -5. There are no options here greater than 5 though, so it is not possible.

Although I believe the problem should be phrased "Which number is less than -3 and greater than 5."

It's semantics.  Here, the word "or" means either. 

So, is there an answer which is either less than –5 or greater than 5.  

Yes, there is such an answer.  It's #1 because –5 is less than –3. 

It isn't greater than 5 but we don't care, because it said "or" ... as in pick one.  

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