Computing valuations for quintic log Fano planes with an A4 cusp of tangent contact four

For an explicit family of irreducible complex plane quintics with one A4 cusp of tangent contact four and no other singularity, we describe all real valuations of finite log discrepancy computing the stability threshold for every positive log Fano coefficient. Below c = 3/8 the computing ray is the linear-coordinate (1,2) valuation; above it the ray is the (2,5) valuation in (x,y-x^2). At c = 3/8 the projectivized set of computing valuations is exactly the closed interval of monomial weights 2 <= b/a <= 5/2, including the irrational rays. The numerical threshold formula is an established local computation combined with coefficient interpolation; the subject here is its equality locus. A strict local form of the flag argument excludes valuations with centers away from this interval without assuming they are quasimonomial. No classification of the boundaryless coefficient c = 0, and no priority claim beyond the documented source comparison, is asserted.