The Ksp for Zn(OH)2 is 5.0x10^-17 . Determine the molar solubility of zn(OH)2 in a buffer solution with pH of 11.5 ?

You have the ##K_(sp)## expression, which was explained in the other thread http://socratic.org/questions/in-which-of-the-following-aqueous-solutions-would-you-expect-to-agbr-to-have-the168330.

Here we know the ##[OH^-]## value (how; what is the ##pH##?). Therefore you have the tools to solve for ##[Zn^(2+)]##, whose concentration represents the solubility of zinc hydroxide. Remember that hydroxide ion concentration is squared in the ##K_(sp)## expression.

As an extension, it may be speculated that we could reduce the ##[Zn^(2+)]## value to any degree, simply by increasing ##[OH^-]##. Note that at very high levels of ##[OH^-]##, we are likely to form complex ions such as, ##Zn(OH)_4^(2-)## (I assure you this species is real). This is a competing equilibrium that can occur.