To simplify the expression \( 5\sqrt{14} - 4\sqrt{56} \), we'll start by simplifying the term \( 4\sqrt{56} \).
First, we simplify \( \sqrt{56} \):
\[ \sqrt{56} = \sqrt{4 \times 14} = \sqrt{4} \times \sqrt{14} = 2\sqrt{14} \]
Now, substituting this back into the expression gives:
\[ 4\sqrt{56} = 4 \times 2\sqrt{14} = 8\sqrt{14} \]
Now we can rewrite the original expression:
\[ 5\sqrt{14} - 4\sqrt{56} = 5\sqrt{14} - 8\sqrt{14} \]
Combining the like terms:
\[ (5 - 8)\sqrt{14} = -3\sqrt{14} \]
Thus, the final answer in simplest form is:
\[ \boxed{-3\sqrt{14}} \]