Ratio of the wavelengths of first line of Lyman series and first line of Balmer series is

$5:27$

$\text{wavelength of first line of lymen series } \frac{1}{\lambda_1} = R(\frac{1}{1^2} - \frac{1}{2^2}) = \frac{3R}{4}$

$\Rightarrow \lambda_1 = \frac{4}{3R}$

$\text{wavelength of first line of Balmer series } \frac{1}{\lambda_2} = R(\frac{1}{2^2} - \frac{1}{3^2}) = \frac{5R}{36}$

$\Rightarrow \lambda_2 = \frac{36}{5R}$

$\Rightarrow \frac{\lambda_1}{\lambda_2} = \frac{5}{27}$