To start off with #y# being positive we have to leave it on the left of = and move everything else.

Add #color(blue)(4x)#to both sides. This turns the #-4x # on the left into 0 and you end up with it on the right of = but being positive.

#color(brown)(-4xcolor(blue)(+4x)+5y+16= 0 color(blue)(+4x))#

#0+5y+16=4x#

Subtract #color(blue)(16)# from both sides

#color(brown)(5y+16color(blue)(-16)=4xcolor(blue)(-16))#

#5y+0=4x-16#

Divide both sides by #color(blue)(5)#. This turns the 5 from #5y# into 1 as #5/5=1" and " 1xxy=y#

#color(brown)(5/(color(blue)(5))xxy=4/(color(blue)(5))x-16/(color(blue)(5))#

#y= 4/5x-16/5#