To simplify the expression \( \frac{2}{\sqrt{7}} - \sqrt{5} - \frac{2}{\sqrt{7}} + \sqrt{5} \), we can combine like terms.

First, let's rewrite the expression:

\[ \frac{2}{\sqrt{7}} - \sqrt{5} - \frac{2}{\sqrt{7}} + \sqrt{5} \]

Notice that \( \frac{2}{\sqrt{7}} \) and \( -\frac{2}{\sqrt{7}} \) are like terms, and \( -\sqrt{5} \) and \( \sqrt{5} \) are like terms.

Combine the like terms:

\[ \left( \frac{2}{\sqrt{7}} - \frac{2}{\sqrt{7}} \right) + \left( -\sqrt{5} + \sqrt{5} \right) \]

Both pairs of terms cancel each other out:

\[ 0 + 0 = 0 \]

So, the simplified expression is:

\[ 0 \]