Landing page for the deal is unique per account from what I can see, so can't link to it. But if you're a current Prime subscriber, go to the Amazon.com.au homepage and see if you have the deal I have highlighted.
All you need to do is stream 1 full track on Amazon Music and a $5 off promo code will be emailed to you within 5 days.
Terms and conditions
• Eligible Amazon Prime customers who complete an Amazon Music stream between 09.00am on 20th April 2021 and 11.59pm on 30 June 2021 will receive a $5 promotional code to redeem against a future Eligible Order on Amazon.com.au (the “Offer”).
• The Offer is valid only until 11.59pm 30 June 2021 and only until 940 Amazon Prime customers have satisfied the terms and conditions.
• If you qualify for the Offer, the promo code of $5 will be sent to you via email within 5 days from your first Amazon Music stream, and you can use it immediately for your next Eligible Order over $20 ("Minimum Purchase").
• The Offer only applies to eligible Amazon Prime customers who have been invited by email from Amazon or viewed on site marketing regarding the Offer and who have visited this landing page whilst logged into their Prime account and also completed an Amazon Music stream using the same account before 11.59pm 30 June 2021 For the purposes of these T&Cs, the promotional code may only be redeemed on an Eligible Order over the Minimum Purchase amount within 30 days of receipt of the promotional code. An “Eligible Order” refers to any item “shipped and sold by Amazon AU” and excludes products sold by third party sellers (even if fulfilled by Amazon AU or sold by Amazon UK / Amazon US), digital purchases such as e-books, subscriptions such as Prime video and audible, gift cards and postage or delivery rates.
• The promotional code may be redeemed within 30 days of receipt on eligible orders over the Minimum Purchase amount.
• The Offer is subject to a Minimum Purchase requirement (qualified purchase with a value of over $20 or more):if you remove qualifying items from your shopping cart, so that the combined purchase value of the remaining qualifying items at checkout falls below the Minimum Purchase requirement, the Offer will cease to apply; if you cancel your order for a qualifying item (so that the combined purchase value of the remaining qualifying items falls below the Minimum Purchase requirement), the Offer will cease to apply; and if you return a qualifying item (so that the combined purchase value of the qualifying items you retain falls below the Minimum Purchase requirement), Amazon reserves the right to charge you (using the payment method you used for the original order and without further notice) for the discount you received as part of the Offer.
• This Offer cannot be transferred to another customer account.
• This Offer is only available to customers with paid membership to Amazon Prime (excludes Prime free trials).
• Each eligible Amazon Prime customer may claim a maximum of one Offer.
• The Offer cannot be combined with any other promotion.
• Delivery will be applied to each item in accordance with Amazon AU's standard delivery rates and policies.
• Offer does not apply to orders placed with 1-Click.
• Offer is subject to availability and may be withdrawn or amended without notice.
• Promotional codes have no cash redemption value and are not transferable or assignable.
• If you place an order using a promotional code and then return or cancel that order, the promotional code cannot be refunded or re-used.
• Unless otherwise specified on the landing page of the Offer or by Amazon, promotional codes cannot be used on existing orders and only one promotional code can be redeemed per order.
• Amazon's Conditions of Use and Promotional Code Terms & Conditions apply.
• Amazon reserves the right to cancel or modify the Offer at any time.