a) Check your differentiation. Your second term is wrong.
c) The statement "The normal to C at P is parallel to the line given by the equation y+4x-3=0" tells us that the derivative of y with respect to x at x = 5 is the negative reciprocal of the slope of the given line. So, find the slope of the line , invert it, negate it and equate this to .
i) Solve the resulting equation for .
ii) We are told the xcoordinate of point P is 5, so to find the y-coordinate evaluate .