Haggard–Pearce–Royle conjecture on flow roots above five

Let $G$ be a bridgeless graph, and let $\Phi_G(Q)$ denote its flow polynomial. Haggard–Pearce–Royle conjecture. For any bridgeless graph $G$,

$$\Phi_G(Q)>0\qquad\text{for }Q\in[5,\infty).$$

This is a proposed weakening of Welsh's conjecture after the explicit counterexample to the interval $(4,\infty)$; it retains the endpoint $Q=5$ in accordance with Tutte's five-flow conjecture.