S + 4 = 2*(A+4) + 2     (1)    ("4 years from now, Sam will be 2 more than twice Andrew's age.")
S - 5 = 3*(A-5).        (2)    ("5 years ago, Sam was three times Andrew's age.")


From (1), express S = 2A + 6 and substitute it into (2). You will get

(2A+6) - 5 = 3*(A-5)  ====>

2A + 1 = 3A - 15  ====>  A = 16.


Thus Andrew's present age is 16 years.

The Lauren's present age is 2*16 - 3 = 29 years.

If what's meant is: "Lauren is 3 less than twice Andrew's age. 4 years from now, Sam will be 2 more than twice Andrew's age, then. 5 years ago, Sam was three times Andrew's age, then," 

then Lauren is now 29 years-old, and 5 years ago, was:  

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