Let x be the numerator;  then the denominator is (x+5) and the fraction is  .

They want you solve this inequality

     < .     (1)


                        +---------------------+
                        |     Attention (!)   |
                        +---------------------+


     Do not multiply both sides by (x+5), because you don't know in advance, 
                  if this value is positive or negative.


    +----------------------------------------------------------------------+
    |   THERE IS ANOTHER METHOD TO SOLVE IT without making wrong steps !   |
    +----------------------------------------------------------------------+


Re-write equation (1)  equivalently  in this form

     -  < 0.


Write it with the common denominator, which is  5*(x+5).

     -  < 0.


Simplify

     < 0,

     < 0,

     < 0.


This inequality is equivalent to

     < 0.


The last inequality is hold in these two cases:

    (a)  3x-10 < 0  and  x+5 > 0

or 

    (b)  3x-10 > 0  and  x+5 < 0.



In case (a),  it implies  3x < 10  and  x > -5,  which is the same as  x < 10/3  and  x > -5,

              which gives the answer -5 < x < 10/3.


In case (b),  it implies  3x > 10  and  x < -5,  which  has no solutions.


ANSWER.  The solution set is  -5 < x < 10/3,  or,  in interval form,  (-5, 10/3).