The Borodin–Kostochka Conjecture states that for a graph G $G$ , if Δ ( ) ≥ 9 ${\rm{\Delta }}(G)\ge 9$ and ω ≤ − 1 $\omega (G)\le {\rm{\Delta }}(G)-1$ then χ $\chi . We prove the P 5 gem $({P}_{5},\text{gem})$ -free graphs, is, graphs with no induced ${P}_{5}$ K ∨ 4 ${K}_{1}\vee {P}_{4}$