Why P2O5 does not show oxidising properties while N2O5 is the strongest oxidising agent among pnictogen oxides?
A very easy half-answer would base this on electronegativity.

Nitrogen’s electronegativity is $\approx 3$ while phosphorus’ is $2.19$. Oxygen’s is, of course, $3.5$. So the electronegativity difference between nitrogen and oxygen is much lower, meaning that oxygen is much less able to stabilise nitrogen’s high oxidation state.

Contrarily, phosphorus’ low electronegativity means oxygen can stabilise its high oxidation state rather well and the compound is much less likely to act as an oxidating agent by itself.