Answer:
1.  y = -(2/5)x - (1/5)
2. y = -(9/5)x - 4
Step-by-step explanation:
For 1: 
Step 1:  rewrite the equation of the given line in to slop-intercept form by solving for y
  2x + 5y = 15    
      5y = -2x + 15               (subtract 2x from both sides)
         y = -(2/5)x + 3           (divide both side by 5)
Step 2:  Our line is parallel to this line, so it has the same slope, but a different  y-intercept, so set up the equation...
   y = -(2/5)x + b      
 We are given a  point (x, y) of (2, -1), so plug that in and solve for b. 
  -1 = -(2/5)(2) + b
     -1 = -4/5 + b      (simplify)
         4/5 -1 = b      (add 4/5 to both sides to isolate b)
         4/5 - 5/5 = b
              -1/5 = b             
So the equation of our line is  y = -(2/5)x - (1/5)
For 2:  
Step 1:  Perpendicular lines have slopes that are opposite reciprocals of each other.  That means you take the slope, flip the fraction, and change the sign.
Here our given line is y = (5/9)x - 4 so the slope 5/9
The opposite reciprocal of 5/9 is -9/5
We set up the equation
y = -(9/5)x + b      
   we are given a point (x, y) of (-5, 5), so plug that in and solve for b
5 = -(9/5)(-5) + b
     5 = 9 + b
      -4 = b  
So our equations is  y = -(9/5)x - 4