Let the number of men required to complete the work in $6k$ days be denoted by $m$. According to the problem, this number of men can complete the work in $6k$ days.

The relationship between the number of men and the time taken to complete the work can be described by the formula:

Men × Time = Work (constant)

So, initially:

$m \times 6k =$ constant work

Let the new number of men be $n$. According to the formula, for the work to be completed in $5k$ days:

$n \times 5k =$ constant work

Since the work is constant, we can equate the two expressions for the work:

$m \times 6k = n \times 5k$

Simplifying this:

$n = \frac{6}{5} \times m$ Percent increase $= (n - m) / m \times 100 = ((\frac{6}{5})m - m) / m \times 100 = (\frac{1}{5}) \times 100 = 20\%$

Thus, the number of men should be increased by $20\%$ to complete the work in $5k$ days.