To solve the expression \((2^{2 \cdot 2^3 \cdot 2^4}) : 2^5(2^{2 \cdot 2^3 \cdot 2^4}) : 2^5\), we first need to understand and simplify it.

Firstly, we simplify the exponents inside the base 2 terms:
- The expression inside the parentheses is \(2^{2 \cdot 2^3 \cdot 2^4}\).

Now, simplify the exponent:
- \(2 = 2^1\)
- So, \(2^3 = 8\) and \(2^4 = 16\),
- Therefore, \(2^3 \cdot 2^4 = 8 \cdot 16 = 128\),
- So, \(2 \cdot 128 = 256\),
- Therefore, the exponent simplifies to \(2^{256}\).

Now let’s restructure the expression:
- We have \(2^{256} : 2^{5+256} : 2^5\).

The entire expression boils down to:
1. \((2^{256})\) : \((2^{261})\) : \((2^5)\).

If we simplify \((2^{256}) : (2^{261}) : (2^5)\), we apply the properties of exponents:
- \((2^{256}) : (2^{261})\) simplifies to \(2^{256-261} = 2^{-5}\),
- \(2^{-5} : 2^5\) simplifies to \(2^{-5-5} = 2^{-10}\).

Thus, the simplified result of the entire expression is \(\frac{1}{2^{10}}\) or \(2^{-10}\).