Bike Frame size

My opinion as a casual observer to the industry is that TT bikes and tri bikes are now very different, and each is their own category where maybe 5 years ago they were one joint category. Triathlon bikes often have slightly more relaxed fit geometries to accomodate the longer distances and durations of triathlons (up to 112 mi for IM) vs TTs, which are often much much shorter (5 to 25 mIles maybe?). Tri bikes also have nutrition and storage features or capabilities integrated into their design, again to accommodate the longer time spent in the saddle. For instance, specialized makes the shiv and the shiv TT. And the bikes are incredibly different.

The question of what size is right for you is a complicated one. Some will tell you to get a $350 bike fit before even considering what brand or frame size to get, others may tell you to just Google what size you might be. If a bike fit isn't a budgetary problem, it's probably a good idea. If it is, there's lots of resources out there to research to try to make an educated purchase. GENERALLY, (don't skewer me, BT), 5 9 is in the middle of size ranges and you'd be looking at 52-54cm frames, or medium. But, could be different based on your anatomy/flexibility.