  We compute the rational points on the Atkin-Lehner quotient $X^+_0(125)$
using the quadratic Chabauty method. Our work completes the study of
exceptional rational points on the curves $X^+_0(N)$ of genus between 2 and 6.
Together with the work of several authors, this completes the proof of a
conjecture of Galbraith.
