Answer
$2.25mm$
Work Step by Step
To find the distance between bright fringes, use the double-slit equation of $dsin\theta=m\lambda$, where $m=1$. Since the distance from the screen to the slit is incredibly large compared to the distance between the slits, a small-angle approximation of $sin\theta \approx tan\theta \approx \theta$ can be used, so that $\sin \theta = \frac{y}{L}$.
This leaves: $$\frac{dy}{L}=\lambda$$ Solving for the distance between fringes $y$ yields: $$y=\frac{\lambda L}{d}=\frac{(500 \times 10^{-9}m)(5.40m)}{1.20\times 10^{-3}m}=2.25mm$$
