Yes, the 109.5 mm BB-5500 is a V1 (road) Octalink bottom bracket meant for a 9-speed era Shimano double crank, the 105 FC-5500 or Ultegra FC-6500 or Dura Ace FC-7700. No other crank design will fit. The BB-5500/BB-6500 series bottom brackets also came in 118.5 mm spindle lengths to match the triple cranks of these models.

As noted, these are now obsolete models and you will have to find the cranks either used or NOS. As further noted, you seem to have a "cart-before-the-horse" problem as the usual procedure is to pick the crank and then choose the matching bottom bracket.