解$:(1)$根据题意,得$5 * (-5) = 3×5 - 4×(-5) = 35;$
$ (2)$因为$x * (x - 3) = 1,$
所以$3x - 4(x - 3) = 1,$
$ $去括号得$3x - 4x + 12 = 1,$
$ $移项得$3x - 4x = 1 - 12,$
$ $合并同类项得$-x = -11,$
$ $系数化为$1$得$x = 11;$
$ (3)$因为$2 * (2 * x) = -34,$
所以$3×2 - 4×(3×2 - 4x) = -34,$
$ $即$6 - 4(6 - 4x) = -34,$
$ $去括号得$6 - 24 + 16x = -34,$
$ $移项得$16x = -34 + 24 - 6,$
$ $合并同类项得$16x = -16,$
$ $系数化为$1$得$x = -1。$