To simplify the expression \(-5\sqrt{7} + 7\sqrt{28}\), we start by simplifying \(\sqrt{28}\).
We know that:
\[ \sqrt{28} = \sqrt{4 \cdot 7} = \sqrt{4} \cdot \sqrt{7} = 2\sqrt{7} \]
Now we can substitute \(\sqrt{28}\) with \(2\sqrt{7}\) in the expression:
\[ -5\sqrt{7} + 7\sqrt{28} = -5\sqrt{7} + 7(2\sqrt{7}) \]
Now, let's simplify this further:
\[ = -5\sqrt{7} + 14\sqrt{7} \]
Next, we can combine the like terms:
\[ = (-5 + 14)\sqrt{7} = 9\sqrt{7} \]
Thus, the simplified form of the expression is:
\[ \boxed{9\sqrt{7}} \]