To add the polynomials \(3 - 2p - 5p^2\) and \(p^4 - 3p + 4\), we combine like terms.
1. Write down the expressions:
\[
3 - 2p - 5p^2
\]
and
\[
p^4 - 3p + 4
\]
2. Align the terms by their degrees:
\[
p^4 + 0p^3 - 5p^2 - 2p + 3
\]
\[
0 + 0 + 0 + (-3p) + 4
\]
3. Combine the like terms:
- For \(p^4\): \(p^4\)
- For \(p^3\): \(0\) (there's no \(p^3\) term)
- For \(p^2\): \(-5p^2\)
- For \(p\): \(-2p - 3p = -5p\)
- For the constant: \(3 + 4 = 7\)
Putting it all together, the result is:
\[
p^4 - 5p^2 - 5p + 7
\]
Thus, the correct answer is:
\[
\boxed{p^4 - 5p^2 - 5p + 7}
\]