Find the equation of the line through the point $(5,-8)$ that is parallel to the line with equation $-10 x-6 y=-62$. The equation is (Be sure to enter your answer as an equation)

Step 1 ：Given the equation of the line is \(-10x - 6y = -62\).

Step 2 ：Rearrange the equation to the form \(y = mx + c\), we get \(y = \frac{5}{3}x + \frac{31}{3}\).

Step 3 ：The slope of the given line is \(-\frac{5}{3}\).

Step 4 ：Since the line we are looking for is parallel to the given line, its slope is also \(-\frac{5}{3}\).

Step 5 ：Using the point-slope form of the line equation, \(y - y_1 = m(x - x_1)\), where \((x_1, y_1)\) is the given point \((5,-8)\) and \(m\) is the slope \(-\frac{5}{3}\), we can find the equation of the line.

Step 6 ：Substitute the values into the equation, we get \(y + 8 = -\frac{5}{3}(x - 5)\).

Step 7 ：Simplify the equation to the standard form, we get \(5x + 3y = 1\).

Step 8 ：Final Answer: The equation of the line through the point \((5,-8)\) that is parallel to the line with equation \(-10 x-6 y=-62\) is \(\boxed{5x + 3y = 1}\).