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Let's say the number of comic books on each shelf is x.
The total number of comic books in the shelves is 5*x.
When Jose's father adds 20 books, the number of books on the bottom shelf becomes x + 20.
So, the total number of books on all the shelves is x + (x + x + x + x + 20) = x + x + x + x + 20 = 5*x + 20.
We are given that 5*x + 20 = 125.
Subtracting 20 from both sides of the equation, we get 5*x = 125 - 20 = 105.
Dividing both sides by 5, we get x = 105/5 = <<105/5=21>>21.
The total number of books in Jose's collection is 5*x = 5*21 = <<5*21=105>>105 books. Answer: \boxed{105}.