Solution:

Total effort required by 5 painters for 19 days = 5 × 19 = 95 man-days.

Initial effort by 5 painters for 9 days = 5 × 9 = 45 man-days.

Job still requires 95 − 45 = 50 man-days, and there are 25 painters available to do it.

Additional effort required by 25 painters for 50 man-days = 50 / 25 = 2 days.

Thus, 2 more days are required to complete the painting job.

Alternative Shorter Solution:

5 painters require 19 − 9 = 10 more days to complete the job.
Therefore, 5 + 20 = 25 painters will require 10 × 5 / 25 = 2 more days to complete the job.

Food for thought:

The number of days for the job is inversely proportional to the number of painters. So, is 'number of days × number of painters = constant'?

What assumptions were made to arrive at the solution?
Is something assumed about the output of the painters?