Clues 2-5 almost form a cyclic symmetric group. I'm going to add a six clue "The only topping Brenda and Clara had in common was olives."

Now for each person take the two clues mentioning them.  For example Anna: "The only topping Anna and Brenda had in common was pepperoni." and "The only topping Anna and Daniella had in common was green pepper."

So we know Anna has at least pepperoni and green pepper.  But then that means Daniella cannot have had pepperoni and Brenda cannot have had green pepper.

Similar analysis from Brenda gives us Clara cannot have had pepperoni and Anna could not have had olives.

From Clara: Elena cannot have had olives and Brenda cannot have had sausage.

From Daniella: Anna cannot have had mushrooms and Elena cannot have had green peppers

From Elena: Daniella cannot have had sausage and 

Then each lady has two ingredients they cannot have had. 

Anna cannot have had mushrooms or olives.

Brenda cannot have had sausage or green pepper.

Clara cannot have had pepperoni or mushrooms.

Daniella cannot have had sausage or pepperoni.

Elena cannot have had olives or green peppers.

With two ingredients excluded from each then they must have had all three other ingredients.  Then:

Anna had sausage, pepperoni, and green pepper.

Brenda had pepperoni, mushroom, and olives.

Clara had sausage, olives, and green pepper.

Danielle had mushroom, olives, and green pepper.

Elena had sausage, pepperoni, and mushroom.