证明: (1)
∵ $BC:DE=40:24=5:3,$$AB:AD=25:15=5:3,$$AC:AE=20:12=5:3,$
∴ $BC:DE=AB:AD=AC:AE。$
∴ $\triangle ABC \sim \triangle ADE$
(2)
∵ $\triangle ABC \sim \triangle ADE,$
∴ $\angle BAC = \angle DAE = 125^\circ。$又
∵ $\angle EAC = 70^\circ,$
∴ $\angle CAD = \angle DAE - \angle EAC = 55^\circ$