To simplify the expression \(\sqrt{2} + \sqrt{3} + \sqrt{4} + \sqrt{5}\), we can start by simplifying any terms that are perfect squares.

\(\sqrt{4}\) is a perfect square, and it simplifies to 2:
\[
\sqrt{4} = 2
\]

So the expression becomes:
\[
\sqrt{2} + \sqrt{3} + 2 + \sqrt{5}
\]

The terms \(\sqrt{2}\), \(\sqrt{3}\), and \(\sqrt{5}\) are irrational numbers and cannot be simplified further. Therefore, the simplified form of the expression is:
\[
\sqrt{2} + \sqrt{3} + 2 + \sqrt{5}
\]

If you need a numerical approximation, you can use the approximate values of the square roots:
\[
\sqrt{2} \approx 1.414, \quad \sqrt{3} \approx 1.732, \quad \sqrt{5} \approx 2.236
\]

Adding these approximations together:
\[
1.414 + 1.732 + 2 + 2.236 \approx 7.382
\]

So, the approximate value of \(\sqrt{2} + \sqrt{3} + 2 + \sqrt{5}\) is about 7.382.