Solution:

Given that the thermal resistance is the same for both rods, we have the equation:

\[
\frac{L_1}{K_1} = \frac{L_2}{K_2}
\]

So, the ratio of lengths is:

\[
\frac{L_1}{L_2} = \frac{K_1}{K_2}
\]

If the ratio of the thermal conductivities \(K_1:K_2 = 5:4\), the ratio of the lengths will be the same:

\[
\frac{L_1}{L_2} = \frac{5}{4}
\]

Therefore, the correct ratio of the lengths is \(5:4\).