First, put the equations into slope-intercept form(y = mx + b):
[tex] 4x+5y=15\\5y=-4x+15\\y=\frac{-4}{5}x+3\\\\ 12x+15y=0 \\15y=-12x\\ y= \frac{-12}{15}x=\frac{-4}{5}x\\
y=\frac{-4}{5}x[/tex]
Since slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept, the slope of the line(value of m) determines whether the lines are parallel or perpendicular.
Parallel lines have the same slope, and since [tex] \frac{-4}{5}=\frac{-4}{5} [/tex], the lines are parallel. Also, because the m's aren't the same, the lines aren't identical.
Your answer is parallel.
