Let S be the volume of the 100 mg/L stock solution required (in milliliters), and

let D be the volume of the diluent required.


Then

S + D = 20,        (1)    (counting the total liquid volume)

 = 5.     (2)    (counting the concentration of the resulting mixture in milligrams per milliliters)



Simplify (2) to

100*S = 5*20 = 100,


which implies  S =  = 1.


Then from equation (1),  D = 20 - S = 20 - 1 = 19.


Answer.   1 milliliter of the 100 mg/mL  stock solution and  19 mL of the diluent is required.

To dilute  the  100 mg/ML stock solution  to the concentration of  5 mg/mL,  you should have one volume of  the stock solution  

per 20 volumes of the total liquid.



In other words, you need to add 19 volumes of the diluent to each one volume of the original stock solution, 
and then you will have totally 20 volumes of the mixture of the required concentration.



In our case 20 volumes are exactly 20 milliliters, which means that you need 1 milliliter of the stock solution and 19 milliliters of the diluent.