There are so many ways to say this in German and we mix it all the time, though some ways are more prevalent in certain areas. I'm leaving out the 'regular' version of just saying the numbers and such and there's also the fact that depending on situation (or how you feel that very second) you'll just say 4:20 or 16:20.
4:05: 5 past 4
4:10: ten past 4
4:15: quarter past 4
4:15: quarter 5
4:20: ten to half 5
4:20: 20 past 4
4:30: half 5
4:35: 5 past half 5
4:40: 10 past half 5
4:40: 20 to 5
4:45: quarter to 5
4:45: 3 quarters 5
4:50: ten to 5
5:00: "full"
Sometimes the actual hour is implied in a question/conversation and you just want to say that it's the full hour you're talking about and just say "Voll" or "Um". Same works with "Halb" and "ten to half" if the hour is not important or implied by context, which you can't do if you just say the numbers.
EDIT: speaking of forgetting some. While it's customary to say "10 past 4" usually nobody says "15 past 4" and instead uses "four fifteen" (actually "vier Uhr fuenfzehn") or "quarter past 4" and then at 4:20 it's "20 past 4 again".