To simplify the expression \((5^5 - 5^4)^3 / 50^6\), let's break it down step by step.

First, simplify the numerator \(5^5 - 5^4\):

\[ 5^5 = 5 \cdot 5 \cdot 5 \cdot 5 \cdot 5 = 3125 \]
\[ 5^4 = 5 \cdot 5 \cdot 5 \cdot 5 = 625 \]

So,

\[ 5^5 - 5^4 = 3125 - 625 = 2500 \]

Now, the expression becomes:

\[ \left(2500\right)^3 / 50^6 \]

Next, simplify \(50^6\):

\[ 50 = 5 \cdot 10 \]
\[ 50^6 = (5 \cdot 10)^6 = 5^6 \cdot 10^6 \]

Since \(10 = 2 \cdot 5\),

\[ 10^6 = (2 \cdot 5)^6 = 2^6 \cdot 5^6 \]

So,

\[ 50^6 = 5^6 \cdot 2^6 \cdot 5^6 = 5^{12} \cdot 2^6 \]

Now, rewrite \(2500\) in terms of powers of 5 and 2:

\[ 2500 = 25 \cdot 100 = 5^2 \cdot (10^2) = 5^2 \cdot (2 \cdot 5)^2 = 5^2 \cdot 2^2 \cdot 5^2 = 5^4 \cdot 2^2 \]

So,

\[ (2500)^3 = (5^4 \cdot 2^2)^3 = 5^{12} \cdot 2^6 \]

Now the expression is:

\[ \frac{5^{12} \cdot 2^6}{5^{12} \cdot 2^6} \]

Since the numerator and the denominator are the same, the expression simplifies to:

\[ 1 \]

Therefore, the simplified value of the expression \((5^5 - 5^4)^3 / 50^6\) is:

\[ \boxed{1} \]