解：?$(1)$?∵點?$A$?在?$y$?軸上，∴其橫坐標(biāo)為?$0，$?即?$3a - 5 = 0，$?解得?$a = \frac 53$?
此時點?$A$?的縱坐標(biāo)為?$a + 1 = \frac 53 + 1 = \frac 83，$?∴點?$A$?的坐標(biāo)為?$(0，$??$\frac 83)$?
?$ (2)$?∵點?$A$?到?$x$?軸的距離是?$2，$?∴點?$A$?縱坐標(biāo)的絕對值為?$2，$?即?$|a + 1| = 2$?
當(dāng)?$a + 1 = 2$?時，?$a = 1，$?此時點?$A$?的橫坐標(biāo)為?$3×1 - 5 = -2，$?坐標(biāo)為?$(-2，$??$2)$?
當(dāng)?$a + 1 = -2$?時，?$a = -3，$?此時點?$A$?的橫坐標(biāo)為?$3×(-3) - 5 = -14，$?坐標(biāo)為?$(-14，$??$-2)$?
綜上，點?$A$?的坐標(biāo)為?$(-2，$??$2)$?或?$(-14，$??$-2)$?
