I am a 15 year old girl and 5'5 in height.
How can I increase my height in terms of food and exercise? Is there some specific diet plan or routine practice required that could accomplish this? I would like to be at least 5'7.
You're 15, you still have several years of development left. There's no magical panacea that will suddenly give you a few inches of height, platform shoes or heels not withstanding.
Height is determined by genetics, primarily. However, maintaining a healthy diet, low in processed foods, and keeping yourself fit and active will allow your body to grow to it's fullest potential.