After 5 days, Sara has baked 5 days * 10 cakes/day = <<5*10=50>>50 cakes.
After Carol's feast, there are 50 cakes - 12 cakes = <<50-12=38>>38 cakes remaining.
Sara needs 2 cans/cake * 38 cakes = <<2*38=76>>76 cans of frosting.
#### 76