To identify the incorrect statement, let's analyze each option:$\\$Option 1: $\\$All the five 5d orbitals are different in size when compared to the respective 4d orbitals.$\\$This statement is correct because 5d orbitals are larger than 4d orbitals due to the higher principal quantum number.$\\$Option 2: $\\$All the five 4d orbitals have shapes similar to the respective 3d orbitals.$\\$This statement is correct because the shape of orbitals is determined by the azimuthal quantum number (l), which is the same for 3d and 4d orbitals.$\\$Option 3: $\\$In an atom, all the five 3d orbitals are equal in energy in the free state.$\\$This statement is correct because in a free atom (not in a magnetic or electric field), all orbitals of the same subshell have the same energy (degenerate).$\\$Option 4: $\\$The shapes of $d_{xy}, d_{yz}, d_{zx}$ orbitals are similar to each other; and $d_{x^2-y^2}, d_{z^2}$ orbitals are similar to each other.$\\$This statement is incorrect. While $d_{xy}, d_{yz},$ and $d_{zx}$ orbitals have similar shapes (cloverleaf), $\\ d_{x^2-y^2}$ is also cloverleaf-shaped but oriented differently, and $d_{z^2}$ has a unique shape with a donut around the z-axis.$\\$Therefore, the incorrect statement is Option 4.