Since A, B , C are the angles of a triangle and we know that the sum of all angles in a triangle is 180 degrees .

Consider A =5x

B=1x

C=6x

5x+1x+6x=180

12x=180

x=15 degrees

Angles A=5 X 15=75 degrees

B=15 degrees & C= 6X15= 90 degrees

By sine rule  we know that (a/sinA)=(b/sinB)=(c/sinc)=2R

hence a=2RsinA, b=2RsinB, c=2RsinC

a:b:c=2RsinA : 2RsinB : 2RsinC

=sinA : sinB : sinC

=sin75 : sin15 : sin90