Step 1: Crystal field splitting in octahedral complexes.
In an octahedral complex, the five d orbitals split into two sets: lower-energy $t_{2g}$ (3 orbitals) and higher-energy $e_g$ (2 orbitals), separated by the splitting energy $\Delta_o$.
Step 2: Condition $\Delta_o < P$.
When $\Delta_o$ is less than the pairing energy $P$, it costs more energy to pair two electrons in the same $t_{2g}$ orbital than to promote an electron to the higher $e_g$ orbital.
Step 3: Electron filling for $d^5$.
Electrons follow Hund's rule: each of the five d orbitals gets one electron before any pairing occurs. Three electrons enter $t_{2g}$ (one each) and two electrons enter $e_g$ (one each). All five electrons are unpaired.
Step 4: Electronic configuration.
The electronic configuration is $t_{2g}^3~e_g^2$ (high-spin). This complex has 5 unpaired electrons and is strongly paramagnetic. The configuration for a $d^5$ ion when $\Delta_o < P$ is $t_{2g}^3~e_g^2$.