Does silver dissolve in water

"No, it is insoluble in water."

But if you are looking for more specifics: Silver chloride is soluble in water, just at very low concentrations. The solubility product is 1.8 X 10^(-10), which is equal to *pK value of -9.75.

According to Wikipedia, the solubility of silver chloride in water is 520 micrograms per 100g (mL) of water at 50 oC. For all intents and purposes, silver chloride is insoluble in water.