Step 1 :The component form of a vector is simply the coordinates of the point it ends at, assuming it starts at the origin. In this case, the vector \(\mathbf{v}\) ends at the point (2,5), so its component form is simply (2,5).
Step 2 :The magnitude of a vector is the length of the vector, which can be calculated using the Pythagorean theorem. In this case, the magnitude of \(\mathbf{v}\) is \(\sqrt{2^2 + 5^2}\).
Step 3 :Final Answer: The component form of the vector \(\mathbf{v}\) is \(\boxed{(2, 5)}\) and its magnitude is \(\boxed{5.385164807134504}\).