First the good news :) Yes, it may be possible to increase your height via stretching exercises by about 1 to 2 inches with dedication and hard work.
Now the bad news :( It's not permanent!
Let’s look at what makes you the height your are
The height you are is determined by the genes you inherit from your mom and dad, as well as the diet and nutrition you received when you were in your growth phase. You grow most before you're born, in the womb, (about 20 inches) and then at a steady rate during your childhood.
During puberty you have a growth spurt, and boys will outstrip girls in height by about 5-6 inches by the time they reach adulthood.
Interestingly, your bones stop growing at different times! Feet and hands stop first, then legs and arms. Then the spine. You stop growing when you are through puberty and enter adulthood. (If you are a early developer you will stop before your friends who are late developers). The growth plates fuse and you cease growing.
Some people have growth hormone deficiency which is a medical condition, caused by problems in the pituitary gland, causing the body to produce insufficient growth hormone.
Lionel Messi, the Argentinian footballer who plays for FC Barcelona was diagnosed with this when he was 11. He received treatment (paid for by FC Barcelona) and is now 5ft 7in. (Being on the short side hasn't stopped him being world footballer of the year!!)
Growth hormone won't help you though - at 17 it is too late.
There is an operation you can have to make you taller. A surgeon will lenghten the bones in the leg. It is painful, takes forever and costs a fortune (you won't get it on the NHS).
I’ve read about some stretching exercises you can do that ‘guarantee’ you will gain height! Here is the video - but please remember - they do not guarantee you will remain taller. Unless you can make your bones longer you cannot grow taller. I think a lot of it is down to good posture.
Every reputable medical opinion I’ve ever read will tell you this is a Tall Tale!