Write the equation of a sine function that has the following characteristics.
Amplitude: 5 Period: $5 \pi$ Phase shift: $\frac{1}{7}$
Type the appropriate values to complete the sine function.
\[
y=5 \sin \left(\frac{2}{5} x-\square\right)
\]
(Use integers or fractions for any numbers in the expression. Simplify your answers.)

Step 1 ：The given function is of the form $y = A \sin(Bx - C)$, where $A$ is the amplitude, $B$ is the frequency, and $C$ is the phase shift.

Step 2 ：The amplitude is given as 5, which is the coefficient of the sine function.

Step 3 ：The period of the function is given as $5\pi$. The period of a sine function is given by $\frac{2\pi}{B}$. So, we can set up the equation $\frac{2\pi}{B} = 5\pi$ and solve for $B$.

Step 4 ：Dividing both sides of the equation by $\pi$, we get $\frac{2}{B} = 5$.

Step 5 ：Multiplying both sides by $B$ and then dividing by 5, we get $B = \frac{2}{5}$.

Step 6 ：The phase shift is given as $\frac{1}{7}$. This is the value of $C$ in the function.

Step 7 ：So, the equation of the sine function with the given characteristics is $y = 5 \sin \left(\frac{2}{5} x - \frac{1}{7}\right)$.

Step 8 ：Checking the function, we see that it has the correct amplitude, period, and phase shift.

Step 9 ：Therefore, the final answer is $\boxed{y = 5 \sin \left(\frac{2}{5} x - \frac{1}{7}\right)}$.