It does not exist because the function is not continuous at -2.
Substitute -2 into both rules and they must equal the same number.
USING a TI-83 plus press Y= in Y1 put (2x+5)(x<-2) and in Y2 put (x+4)(x≥-2)
Arrow over in front Y1 and press ENTER until you see only 3 diagonal dots
Do the same in front of Y2.
Inequality signs are under 2nd MATH
Press GRAPH (You can see it is not continuous at -2)