Puzzle n°11 (***) - The (almost) Desert Island

Five big cats (a Maine Coon, a Norwegian Forest Cat, a Pixie Bob, a Ragdoll and a Siberian)
are stranded on an island which they thought was a desert island...
In fact, a little Abyssinian lives on this island, and he eats mice which are to be found in quite large quantities.

Not aware of our little Aby, our 5 castaways decide to gather all the mice of the island,
in order to breed them and have enough food until someone comes to rescue them.
They manage to do so, and then fall asleep after this tiring chase,
having decided that they would split their flock between them the next day.

But, in the middle of the night, the Maine Coon wakes up and decides to take his share right away.
The little Aby hears some noise and wakes up too.
This makes him hungry, he catches one mouse and eats it without being seen by the Maine Coon,
who hides a fifth of all remaining mice for his personal use and goes back to sleep.

Some time later, the Norwegian Forest cat wakes up.
The same scenario happens again : the little Aby wakes up, eats a mouse without being heard or seen,
and the Norwegian cat, not knowing that the Maine Coon has already taken his share,
hides away a fifth of the remaining mice for his personal use and goes back to sleep.

It's now the Pixie Bob's turn to wake up... The little Aby eats yet another mouse,
then the Pixie Bob takes away a fifth of all remaining mice...
Then the same thing happens again with the Ragdoll...
And then again with the Siberian !

Hence, when they all wake up the next morning, our little aby has eaten 5 mice,
and each one of the 5 castaways has hidden his own little mice flock.
They gather and split the remaining group of mice into 5 equal parts, one for each of them.
There are no mice remaining after this.

How many mice, at the minimum, were on the island when they arrived ?

If you manage to answer the previous question, try to answer the more general one :
how many mice could there have been on the island when they arrived ? (i.e. find all solutions)

... I'm giving up ...