It depends on how much "room" you have on your existing account. Each battle.net account has room for eight WoW sub-accounts. If you have enough available sub-account "slots" to add what you need, that would probably be best, since you would inherit any pets and mounts and be able to provide heirlooms to your alt accounts. But if you want to start five new accounts and already have used up five or more sub-accounts, you would need to create a new battle.net account.
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