Answer
$y=-\displaystyle \frac{2}{5}x++1$
Work Step by Step
We solve the given equation for y (write it in slope-intercept form)
$2x+5y=15$
$5y=-2x+15$
$y=-\displaystyle \frac{2}{5}x+3$
The slope of the line is $m=-\displaystyle \frac{2}{5}$, and any line parallel to it has the same slope.
Now, find the wanted parallel line.
The point-slope equation of a line containing the point $(x_{1},y_{1})$, with slope $m$ is
$y=y_{1}+m(x-x_{1})$
Given $(x_{1},y_{1})=(5,-1)$ and $m=-\displaystyle \frac{2}{5}$
$y=-1+(-\displaystyle \frac{2}{5})(x-5)$
$y=-1-\displaystyle \frac{2}{5}x+2$
$y=-\displaystyle \frac{2}{5}x++1$
