I did a 30 day push up challenge about 12 months ago. A really cool challenge. The best tips I have for you is yes, do 5 sets or 4 sets throughout the day and count down (19, 18 etc.), not up (1,2, etc) is makes it more bearable as you get to set 4/5. After 30 days, I saw some changes in my chest/arms, but I felt a whole lot stronger.

Rather you reach your goal or not, the is consistency, meaning push-up or work out regularly...say 2-4 times each week....and incorporate Cardio too..I hate cardio so I jump rope instead.