That's impossible for anyone to know, I think.
It's normal for adult males to have an armspan about 2 inches longer than height. You might close the gap on that some and you may even reach 5'10, but my guess (and this is just a wild guess) is that you will probably get to 5'9 before growth levels off.
I'm sure a more educated guess could be made with the proper formulas obtained through clinical studies applied to your history of growth spurts, but we'd need all that historic data and the equation (one exists, but I can't access the journal article that has it).
Is Arm Span an Accurate Measure of Height in Young and Middle-Age Adults? -- Brown et al. 9 (1): 84 -- Clinical Nursing Research
(actually, sorry, that study is for 20-61 age group, but perhaps one exists for 0-18?)