What is the value of:
\(\[ \sqrt{ \frac{ \log_e \left( \sqrt[3]{\frac{e^{10} \cdot 3^5}{2^{12}}} \right)}{\frac{\sqrt{625} - 5}{4}} } \]\)
(Please don't use AI)
\(\[ \sqrt{ \frac{ \log_e \left( \sqrt[3]{\frac{e^{10} \cdot 3^5}{2^{12}}} \right)}{\frac{\sqrt{625} - 5}{4}} } \]\)