5cos(x+85)=sin(x-30),
5sin(90-(x+85))=sin(x-30),
5sin(5-x)=sin(x-30), expand:
5sin(5)cos(x)-5cos(5)sin(x)=sin(x)cos(30)-cos(x)sin(30), divide through by cos(x):
5sin(5)-5cos(5)tan(x)=tan(x)cos(30)-sin(30),
5sin(5)+sin(30)=tan(x)(cos(30)+5cos(5)),
tan(x)=(5sin(5)+sin(30))/(cos(30)+5cos(5))=0.160044 approx,
x=9.093° approx.
But since tangent is periodic (cyclic), x=9.093+180n degrees, where n is an integer.
Therefore x=9.093°, 189.093°, 369.093°, etc.