Q.Why are pentahalides of P, As, Sb and Bi more covalent than their trihalides?

Step 1 — Oxidation states involved.

Trihalides: central atom in +3 state. Pentahalides: central atom in +5 state.

Step 2 — Fajans' rule.

Fajans' rule states that covalent character in a compound increases with (i) increasing charge on the cation and (ii) decreasing size of the cation, because a smaller, more highly charged cation polarises the anion's electron cloud more strongly, pulling electron density toward itself (partial covalent sharing rather than pure ionic-like transfer).

Step 3 — Application here.

Going from the +3 to +5 state, the central atom carries a higher effective positive charge (higher charge density since it's roughly the same/slightly smaller ionic size at higher oxidation state). This higher charge density polarises the halide ions more strongly, pulling the shared electron pair back toward the central atom and increasing the covalent character of the M–X bonds.

Apply Fajans' rule directly: compare the effective charge on the central atom in the +5 vs +3 state, and connect higher charge density to stronger polarisation and hence greater covalency.

• Don't think "more halogens attached = more covalent" is the reasoning — it's specifically the higher oxidation state/charge density on the central atom (Fajans' rule), not simply the count of bonds.
• Don't confuse this with the general covalent-character trend down the group (which instead concerns central-atom size, not oxidation state).