Solution:

Total effort required by 8 painters for 29 days = 8 × 29 = 232 man-days.

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

Job still requires 232 − 40 = 192 man-days, and there are 32 painters available to do it.

Additional effort required by 32 painters for 192 man-days = 192 / 32 = 6 days.

Thus, 6 more days are required to complete the painting job.

Alternative Shorter Solution:

8 painters require 29 − 5 = 24 more days to complete the job.
Therefore, 8 + 24 = 32 painters will require 24 × 8 / 32 = 6 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?