Doubt regarding quadratic sieve

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Is calculating $a^2 \equiv p-5 \pmod{p} $ same as calculating $a^2 \equiv 5 \pmod{p} $ ?My code (using quadratic residue method) returns same answers corresponding to both the equations for any odd prime $p$.

For example :-

For $a^2 \equiv 99986 \pmod{99991} $, my $a$ comes out to be 10104.

For $a^2 \equiv 5 \pmod{99991} $, my $a$ comes out to be 10104.