For \( k \in \mathbb{R} \), let the solutions of the equation \( \cos\!\left(\sin^{-1}\!\left(\operatorname{x cot}\!\left(\tan^{-1}\!\left(\cos\!\left(\sin^{-1} x\right)\right)\right)\right)\right) = k, \; 0<|x|<\dfrac{1}{\sqrt{2}} \) be \( \alpha \) and \( \beta \), where the inverse trigonometric functions take only principle values. If the solution of the equation \( x^2 - bx - 5 = 0 \) are \( \dfrac{1}{\alpha^2} + \dfrac{1}{\beta^2} \) and \( \dfrac{\alpha}{\beta} \) then \( \dfrac{b}{k^2} \) is equal to _______
