# ABC's are hauntin' you

Algebra Level 4

If $\Large \color{#D61F06}{a}+\color{#3D99F6}{b}+\color{#20A900}{c} = 0,$ then $\ \Large \dfrac{\color{#D61F06}{a}^5 + \color{#3D99F6}{b}^5 + \color{#20A900}{c} ^5}{\color{#D61F06}{a}\color{#3D99F6}{b} + \color{#3D99F6}{b}\color{#20A900}{c} +\color{#20A900}{c} \color{#D61F06}{a}}=K\cdot \color{#D61F06}{a}\color{#3D99F6}{b}\color{#20A900}{c}.$ $\Large K \ = \ ?$

Note: Assume that $a,b,c$ are not all 0.

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