Why does self-reference have discriminant 5? Why not 4, or 7, or any other number? This paper provides the complete answer. The axiom σ = 1/(1+σ) has discriminant 5 — this is a mathematical fact about the specific equation, not a choice. Discriminant 4 (σ = 1/(1+σ) with different coefficients) fails because ℚ(√4) = ℚ(2) = ℚ — a rational field with no non-trivial automorphism, no Galois structure, and no geometry. Discriminant 7 would require a coefficient in the equation — a free parameter, breaking uniqueness. Discriminant 5 is the unique discriminant produced by the parameter-free self-referential equation. Five is forced.