I got three 4s and one 5 on my AP tests. I know most applicants at really competitive schools will have 5s on all of their exams. How much will the 4s hurt me? Should I avoid sending these scores?
If you have a high GPA and strong SAT/ACT scores, you shouldn't be concerned. AP scores aren't an especially important factor in admissions decisions unless you score lower than a 3. They're more relevant once you get into college, since most schools allow students to place out of introductory courses or earn credits based on their scores.
A 4 is still a very good score. Many colleges (even the super selective ones) will grant you credit or advanced placement for 4s on certain AP tests. For example, here's a chart that shows Princeton's AP credit policies. You can earn credit for 4s on a few AP tests, and Princeton is one of the most selective colleges in the country.
Your grade in an AP class is more important than your test score. A high grade points to a strong sustained effort over the course of the school year. It will also positively impact your GPA, which is the most important factor in any college admissions decision.