Question 247231
let -n= first integer and -m the second
-n=-m-5
-n(-m)=84
substitute
(-m-5)(-m)=84
m^2+5m=84
complete the square
add (5/2)^2 to both sides

m^2+5m+15/4=84+15/4

m^2+5m+15/4=361/4
factor 
(m+5/2)^2=361/4
get sqrt
m+5/2=+\-19/2
m=-5/2+\-19/2
m=-24/2=-12
m=14/2=7
since we want a negative integer it can't be 7
so we have -12
-12+5=-7