Answer
The unknown wavelength is $~~396~nm$
Work Step by Step
We can write an expression for the angles of the diffraction orders:
$sin~\theta_m = \frac{m~\lambda}{d}$
Let $\lambda_2$ be the unknown wavelength.
We can find the value of $\lambda_2$:
$\frac{(5)~\lambda_2}{d} = \frac{(3)~\lambda_1}{d}$
$\lambda_2 = \frac{(3)~\lambda_1}{5}$
$\lambda_2 = \frac{(3)~(660~nm)}{5}$
$\lambda_2 = 396~nm$
The unknown wavelength is $~~396~nm$
