According to NCERT, the five $d$-orbitals are designated as $d_{xy}, d_{yz}, d_{xz}, d_{x^2-y^2}$, and $d_{z^2}$. The shapes of the first four ($d_{xy}, d_{yz}, d_{xz}, d_{x^2-y^2}$) are similar to each other (double dumbbell or cloverleaf shape), whereas the shape of the fifth one, $d_{z^2}$, is different (doughnut shape/dumbbell with a ring). Therefore, the statement claiming $d_{x^2-y^2}$ and $d_{z^2}$ are similar is incorrect.

Other statements are correct:

• Size increases with principal quantum number ($n$), so $5d$ orbitals are larger than $4d$ orbitals.
• Shapes of orbitals depend on the azimuthal quantum number ($l$), not $n$, so $4d$ and $3d$ have similar shapes.
• In a free isolated atom, all five $d$-orbitals of a specific shell are degenerate (equal in energy) .