What I have read pertains to Australian law. Your country may have different consumer laws; I advise checking with your government's consumer rights/advocacy organisation about your consumer rights.
They did not advertise the limited quantity that they had, and the products were not available in reasonable quantities and for a reasonable period of time. If they sold out within 5 minutes of the sale window opening, it means they did not offer reasonable quantities for sale. Offering to notify consumers when the product is back in full price is arguably the "switch" of the "bait-and-switch".
Here is what the Australian Competition & Consumer Commission has to say:
Bait advertising is the practice of offering items for sale at low prices to attract consumers to a business.
Bait advertising can be a legitimate form of advertising. However, it is illegal to engage in this conduct where goods or services are advertised for sale at a discounted price, and they are not available in reasonable quantities and for a reasonable period at that price.
You must state clearly if the good is in short supply or on sale for a limited time. For example, if your advertisement makes it very clear that goods are available at the discount price for ‘today only’, this will limit your obligations to that day.
Legislation: Australian Consumer Law section 35
If there is not a reasonable chance the offer will be available at the advertised price, you may be in breach of the ACL unless you promptly offer a 'rain check', an acceptable substitute product or take other corrective action.
Example: An electronics retailer runs a campaign advertising 50-inch televisions at a price of $799 for a week-long sale. The retailer usually sells about 30 televisions of this type every week. The retailer only stocks two televisions at the advertised price and refuses to take customer orders.
When customers attempt to buy the television at the advertised price, they are told it is out of stock and offered a more expensive unit for $999. This is likely to be bait advertising as the retailer does not have a reasonable supply of the advertised television.