Why is this a 7th order circuit?
You are missing the mesh/loop which includes the left-most capacitor, the upper capacitor and the right-most capacitor. 11 reactive components - 2 inductor nodes - 2 cap meshes = 7.

If you're feeling up to the challenge you can also attempt to find the transfer function of the circuit (s-domain). The circuit order is whatever is higher: the order of the numerator polynomial or the order of the denominator polynomial.