To simplify the expression \( 8\sqrt{125} - 7\sqrt{80} \), we start by simplifying each square root.
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Simplifying \( \sqrt{125} \): \[ \sqrt{125} = \sqrt{25 \cdot 5} = \sqrt{25} \cdot \sqrt{5} = 5\sqrt{5} \] So, \( 8\sqrt{125} = 8 \cdot 5\sqrt{5} = 40\sqrt{5} \).
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Simplifying \( \sqrt{80} \): \[ \sqrt{80} = \sqrt{16 \cdot 5} = \sqrt{16} \cdot \sqrt{5} = 4\sqrt{5} \] So, \( 7\sqrt{80} = 7 \cdot 4\sqrt{5} = 28\sqrt{5} \).
Now, we can substitute these simplified forms back into the expression:
\[ 8\sqrt{125} - 7\sqrt{80} = 40\sqrt{5} - 28\sqrt{5} \]
Since both terms share the same radical \( \sqrt{5} \), we can combine them:
\[ 40\sqrt{5} - 28\sqrt{5} = (40 - 28)\sqrt{5} = 12\sqrt{5} \]
Thus, the final result is:
\[ \boxed{12\sqrt{5}} \]