Add the polynomial

To add the polynomial expressions \(3 - 2p - 5p^2\) and \(p^4 - 3p + 4\), we combine like terms.

Here are the expressions lined up for addition:

\[
\begin{align*}
& \quad 3 \quad - 2p \quad - 5p^2 \\
+ & \quad 4 \quad - 3p \quad + p^4 \\
\end{align*}
\]

Now we add the corresponding terms:

- **Constant terms:** \(3 + 4 = 7\)
- **Linear terms:** \(-2p - 3p = -5p\)
- **Quadratic term:** \(-5p^2\) (there's no quadratic term in the second polynomial)
- **Cubic term:** There are no cubic terms in either polynomial.
- **Quartic term:** \(p^4\) (there's no quartic term in the first polynomial)

Now, writing it all together, we have:

\[
p^4 - 5p^2 - 5p + 7
\]

Thus, the sum of the polynomial expressions is:

\[
\boxed{p^4 - 5p^2 - 5p + 7}
\]