Most people finish their growth spurts by age 17. While some might experience minimal growth afterward, significant height increases are unlikely.
Based on anecdotal evidence from various online forums and personal accounts, it's possible to experience a small increase in height after 17. One account mentions only growing about an inch after age 18. [^1] Another source notes that growth might continue until 19 or 20 in rare cases. [^9] However, the majority of people will see little to no height increase after 17. [^7]
One account suggests a potential height range of between 6'3" and 6'4" for someone already at 5'5" at 17, but this appears to be an outlier. [^1] This prediction seems overly optimistic given the typical growth patterns indicated in other sources. It's important to consider that genetics significantly influence adult height, and the height of your parents and other family members plays a considerable role.
Considering most growth plates fuse around age 17-18, a small increase, perhaps an inch or two, is possible but not guaranteed. Therefore, expecting to reach a height significantly taller than your current height is not realistic.
[^1]: You should be nearing the end of your growth spurt now, your height will still increase but the rate will slow down; I have only grown about an inch since I was 18. If you were going to be impracticably tall then you would be at least 6'2" already. At a guess I'd say you'll end up between 6'3" and 6'4".07-Jan-2017