Two lines are parallel if and only if their slopes are the same, that is:
[tex]m_1=m_2[/tex]To find the slope of the original line we write it in slope-intercept form.
[tex]y=mx+b[/tex]Then:
[tex]\begin{gathered} 5x+y=-6 \\ y=-5x-6 \end{gathered}[/tex]Comparing the two equations we notice that the slope of the line is -5.
Therefore the parallel line has equation:
[tex]y=-5x-4[/tex]