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To add the polynomial expressions \(3 - 2p - 5p^2\) and \(p^4 - 3p + 4\), we combine like terms as follows:
1. Start with the first polynomial: \(3 - 2p - 5p^2\).
2. Add the second polynomial: \(p^4 - 3p + 4\).
Combining these gives:
\[
p^4 + (-5p^2) + (-2p - 3p) + (3 + 4)
\]
Now, combine the terms:
- The \(p^4\) term remains \(p^4\).
- The \( -5p^2 \) term remains \( -5p^2\).
- Combine the \(p\) terms: \(-2p - 3p = -5p\).
- Combine the constant terms: \(3 + 4 = 7\).
So, the resulting polynomial expression is:
\[
p^4 - 5p^2 - 5p + 7
\]
Thus, the correct response is:
**p^4 - 5p^2 - 5p + 7**.