We are mixing a weaker acid solution with a stronger acid
solution to obtain a medium-strength acid solution.

Let the number of gallons of the weaker 
5% solution be x

Then the number of gallons of the final medium-strength
solution will be x + 20
                                     
                                      Number of  
                         Percent       Gallons
  Type       Number       acid         of PURE
   of          of       expressed       ACID
Solution     gallons   as a decimal   contained
-------------------------------------------------
Weaker          x         0.05          0.05x
Stronger       20         0.10        0.10(20)
------------------------------------------------
Mixture       x+20        0.08      0.08(x+20) 

The equation comes from the column on the right

  

        0.05x + 0.10(20) = 0.08(x+20)

Clear of decimals by multiplying through by 100

             5x + 10(20) = 8(x+20)
                5x + 200 = 8x+160
                     -3x = -40 
                       x = 40/3
                       x = 13 1/3 gallons of 5% acid solution.

Edwin