Yea it's possible, someone already mentioned NBA player Nate Robinson who at 5'9" dunks, and of course there was Spud Webb before him who dunked at a height of 5'7".
However, aside from looking at physically gifted individuals, your problem is that at a height of roughly 5'9", you would need 4'1" in height to reach the 10" rim.
That 4'1" difference in height would signify you would need about a 26-inch vertical jump (this is assuming you're jumping statically, running you you jump higher).
The number itself as to how high you need to jump is dependent on many factors, such as arm length, height, and vertical jump (vertical jump is the only factor you can change).
So to slam dunk, your best option is to go with a vertical jump training program, I recommend you do some research on the available programs, but here is a resource on some of the better programs to choose from:
https://ballamazingly.com/best-vertical-jump-training-programs/
Assuming you have an average vertical jump of 16 to 20 inches, and considering the better jump programs can offer 8+ inches to your vertical, then it's very likely you'll be able to dunk.
That being said, it won't be easy. Good luck!
