Past, present, and everything in between

Algebra Level 5

$\Large \prod_{i=1}^{2^{2015}} \left( \sqrt[2^i]{2015} + \sqrt[2^i]{1995} \right)$

Given that the reciprocal of the product above can be expressed as $\large \dfrac 1d \left( a^{1/2^b} - c^{1/2^b} \right)$ where $a,b,c$ and $d$ are positive integers. What is the value of $\large \dfrac{c \log_2( b) + 5a}{\log_2 (b^d)}?$