Lines are parallel if there slopes are the same or equal. Therefore the slope of the equation x + 5y = 10 can be found below
[tex]\begin{gathered} x+5y=10 \\ 5y=-x+10 \\ y=-\frac{1}{5}x+2 \\ m_1=\text{slope 1=-}\frac{1}{5} \end{gathered}[/tex]The equation that passes through (-5, 7) and slope of -1/5 can be found below
[tex]\begin{gathered} m=\frac{y-y_1}{x-x_1} \\ m=\frac{y-7}{x+5} \\ -\frac{1}{5}(x+5)=y-7 \\ -\frac{x}{5}-1=y-7 \\ y=-\frac{x}{5}-1+7 \\ y=-\frac{x}{5}+6 \end{gathered}[/tex]