Adding up the sides, taking two at a time, we get
5 cm + 19 cm = 24 cm > 20 cm
5 cm + 20 cm = 25 cm > 19 cm
19 cm + 20 cm = 39 cm > 5 cm
So we see that the sum of the pair of sides when added is greater than the third side.
Therefore, we can construct the triangle with these measurements.