Question 65049
((x+3)^2/16)-((y+2)^2/25)=1 - equation of a hyperbola
(-3, -2) - the center
Slope = 5/4 or -5/4, just like you said. 
Now, both asymptotes are going through the center, which means that we have the point we need to write the point-slope form of their equations. 
Therefore, the point-slope of an equation going through (-3,-2) and having the slope 5/4 or -5/4 is: y+2 = 5/4(x+3), respectively y+2=-5/4(x+3). I'll let you do the math. 

Cheers,
Cristiana