Handle these Quadratic Inequalities!

Algebra Level 3

If all the solutions of the inequality \[ { x }^{ 2 }+6ax+5{ a }^{ 2 }\quad \le \quad 0\] are also the solutions of the inequality \[{ x }^{ 2 }-14x+40\quad \le \quad 0\], find the number of integral values of 'a'.

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