Add the polynomial expressions 3−2p−5p^2 and p^4−3p+4.

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

1. Write down both expressions:
\[
3 - 2p - 5p^2
\]
\[
+ \ (p^4 - 3p + 4)
\]

2. Group the terms by their degree:
- \(p^4\)
- \(p^2\)
- \(p\)
- constant

3. Now, combine the like terms:
- The \(p^4\) term: \(p^4\)
- The \(p^2\) term: \(-5p^2\)
- The \(p\) terms: \(-2p - 3p = -5p\)
- The constant terms: \(3 + 4 = 7\)

Putting these together, we have:
\[
p^4 - 5p^2 - 5p + 7
\]

Thus, the final result is:
\[
\boxed{p^4 - 5p^2 - 5p + 7}
\]