Complexity of $(\Delta-1)$-coloring graphs of maximum degree $\Delta$

Suppose we have a graph $$G$$ with maximum degree $$\Delta$$. Deciding if $$G$$ can be colored with $$\Delta$$ colors is easy: Brooks' theorem says that this is always possible, unless $$G$$ is a clique or an odd cycle.

I'm interested in the complexity of coloring $$G$$ with $$(\Delta-1)$$ colors. It is well-known that the case $$\Delta=4$$ is NP-complete, as NP-completeness of 3-coloring graphs of maximum degree 4 is already mentioned in Garey&Johnson's book. I would like to know if similar results are known for other small values of $$\Delta$$. For example, I tried searching for the complexity of $$4$$-coloring graphs of maximum degree $$5$$, but failed to find anything relevant.

Question: For which fixed values of $$\Delta$$ is the complexity of $$(\Delta-1)$$-coloring graphs of maximum degree $$\Delta$$ known?

Motivation: I would have initially thought that, since this is NP-hard for $$\Delta=4$$, it would be NP-hard for all larger values of $$\Delta$$. However, it turns out that this is false! According to the main result of [1], "for sufficiently large $$\Delta$$, any graph with maximum degree at most $$\Delta$$ and no cliques of size $$\Delta$$ has a $$\Delta−1$$ colouring". This implies that for sufficiently large (fixed) $$\Delta$$, the problem is in P by the following simple algorithm: check (in time $$n^{\Delta}$$) if $$G$$ contains a clique of size $$\Delta$$; if it does say NO, otherwise say YES.

Question The above implies that $$(\Delta-1)$$-coloring graphs of max degree $$\Delta$$ is in P for sufficiently large $$\Delta$$. What is the smallest concrete value of $$\Delta$$ for which this problem is known to be in P?

References: [1] A Strengthening of Brooks' Theorem, Bruce Reed, JCTB 1999. https://doi.org/10.1006/jctb.1998.1891