In the single-slit experiment, the displacement of the minima of the diffraction pattern on the screen is given by

(1)
where
n is the order of the minimum
y is the displacement of the nth-minimum from the center of the diffraction pattern

is the light's wavelength
D is the distance of the screen from the slit
a is the width of the slit
In our problem,


while the distance between the first and the fifth minima is

(2)
If we use the formula to rewrite

, eq.(2) becomes

Which we can solve to find a, the width of the slit: