log3(5)+log5(3)-log3(15)*log5(15)
=log3(5)+log5(3)-log3(3*5)*log5(3*5)
=log3(5)+log5(3)-[log3(3)+log3(5)][log5(5)+log5(3)]
=log3(5)+log5(3)-[1+log3(5)][1+log5(3)]
=log3(5)+log5(3)-[1+log3(5)+log5(3)+log3(5)*log5(3)]
=-1-log3(5)*log5(3)
=-1-(lg5/lg3)*(lg3/lg5)
=-1-1
=-2