To add the polynomial expressions \(3 - 2p - 5p^2\) and \(p^4 - 3p + 4\), we will combine like terms.
1. Start by writing both polynomials:
\[
3 - 2p - 5p^2
\]
\[
p^4 - 3p + 4
\]
2. Now, arrange them and add them together:
\[
(3 + 4) + (-2p - 3p) + (-5p^2) + p^4
\]
3. Combine the constant terms:
\[
3 + 4 = 7
\]
4. Combine the \(p\) terms:
\[
-2p - 3p = -5p
\]
5. The \(p^2\) term remains:
\[
-5p^2
\]
6. The \(p^4\) term remains:
\[
p^4
\]
7. Now, put it all together by arranging the terms in descending order of power:
\[
p^4 - 5p^2 - 5p + 7
\]
So, the final expression after adding the two polynomials is:
\[
p^4 - 5p^2 - 5p + 7
\]
The correct answer from the options you provided is:
**p^4 - 5p^2 - 5p + 7**.