the polar coordinates are given by M(x, y), such tha x=rcos(teta), and y=rsin(teta), it was given M(5,5), so 5=rcos(teta) and 5=rsin(teta), the ratio gives us 5/5= cotan (teta), 1= cotan (teta), implies 1= tan(teta), so teta = Pi/4, let's find r
5=rsin(Pi/4)=r . sqrt(2)/2, so r =10/sqrt(2)=10sqrt(2)
finally the polar coordinates are (r, teta) = (10sqrt(2), Pi/4)