It just won't stop...

$\textbf{What is the last digit of:}$

$\huge \color{#D61F06}{1!} \color{#0C6AC7}+\color{#EC7300}{2!} \color{#0C6AC7}+\color{#20A900} {3!} \color{#0C6AC7}+ \color{teal}{4!} \color{#0C6AC7}+ \color{#69047E}{5!} \color{#0C6AC7}{+ ... +} \color{hotpink}{2015!}$

$\textbf{NOTES:}$

• $\text{No need to bash, in fact very simple!}$

• $\text{Implied from above ... NO CALCULATORS!!!}$

• $\LaTeX\text { for life!}$