Solution:

Total effort required by 5 painters for 12 days = 5 × 12 = 60 man-days.

Initial effort by 5 painters for 8 days = 5 × 8 = 40 man-days.

Job still requires 60 − 40 = 20 man-days, and there are 10 painters available to do it.

Additional effort required by 10 painters for 20 man-days = 20 / 10 = 2 days.

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

Alternative Shorter Solution:

5 painters require 12 − 8 = 4 more days to complete the job.
Therefore, 5 + 5 = 10 painters will require 4 × 5 / 10 = 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?