Hi, to me your solution is wrong .
For Vd = 0.7V diode current is equal to Id = (4*0.7V + 5*0.7^2) = 2.8 + 2.45 = 5.25mA
And resistor current Ir = (5V - 0.7V)/200Ω = 21.5mA
So Id is not equal to Ir. and this means that your solution is wrong.
And the correct answer is Vd ≈ 1.51V because this time Id ≈ 4*1.51V + 5*1.51V^2 ≈ 17.4405mA and Ir = (5V - 1.51V)/200Ω ≈ 17.45mA
And since Id≈Ir we have a correct solution.
Additional I plot Id vs Vd and load line