17 push ups is very good.
Most people can't do 5. Not proper press ups when your nose touches the floor but your belly (unless it's a bit porky), chest and middle do not, so you get no rest inbetween anyway.
If you can do 17, I'd do reps of 3-4 and 3-4 sets (3 or 4 push ups, 3 or 4 times) either daily or every other day if you can still feel your arms a day later. Then build up your amount of sets. Then build up the number of reps in a set.
I worked up to around 300 a day in sets of 50 when I worked shifts. Before I started, I could only manage 20.
For comparison, Britains' "Most Dangerous Prisoner" Charles Bronson does 1 minute of press ups first thing in the morning on some days. He'll do about 100 in that minute. He held the World Record for press ups in a minute which was a few over 100. He has held a number of World Record for that type of thing.