QIf I have 5 cards in my banished zone, and I summon a Mistress Hurricane and Nitro Juggler with Silver Thorn Dragon Tamer, Luquier's Fanfare ability, can I give Mistress Hurricane Storm?

AYes. Since both Mistress Hurricane's Fanfare ability and Nitro Juggler's Fanfare ability trigger and become pending at the same time, you may resolve them in any order.

Although you only have 3 cards in your banished zone, you can banish 2 more cards by resolving Nitro Juggler's Fanfare ability first, allowing you to fulfill the condition for Mistress Hurricane's Fanfare ability.