Both smartphones have 5.7in screens and are going on sale earlier in the year than their previous generations.
The new launches follow five successive falls in Samsung Electronics’ quarterly profits.
Analysts say the popularity of mid-range phones from Chinese rivals, and Apple’s shift to bigger iPhones, have dented demand for Samsung’s devices.
However, Samsung remains the world leader in terms of overall smartphone shipments.
The announcements were made at a press conference in New York.
Samsung also revealed that its smart wallet service, Samsung Pay – which allows the phones to trigger payment card transactions.
The service would go live in South Korea on August 20.
Samsung Pay will be extended to the US on September 28 and then to the UK and Spain at an unspecified date.
Like previous versions of the Note, Galaxy Note 5 comes with a stylus – which Samsung says makes it suitable for productivity tasks. But the phone now has metal edges and a glass back to give it a more “premium” feel.
In a change of strategy, Samsung has no plans at present to release the Note 5 in Europe – a decision it says is purely for marketing reasons.
Unlike last year, there is no “edge” edition of the Note.
Instead, the Galaxy S6 Edge Plus is targeted at those who want a “phablet”-sized handset with curved sides.
The “plus” in its name refers to the fact that its screen is both 0.6in larger than the earlier edition and more scratch-resistant.
The Galaxy S6 Edge+ now has an extra gigabyte of memory, taking it up to 4GB of RAM to aid multi-tasking, but uses the same in-house Exynos processor as before.
This marks a change from the S5 Plus, which was the same size but contained a faster processor than the original S5.
The decision to host a standalone press conference for the handsets marks a change of strategy for Samsung.
All the previous versions of the Note were unveiled at Germany’s annual IFA tech show, which is still three weeks away. The S5 Plus was announced last October in a low-key press release.
One of the benefits of announcing the new models together at this point is that it should give Samsung about a month’s lead on Apple – reports suggest the company will update its own smartphones on September 9.
Samsung Galaxy S6 Edge+ and the Galaxy Note 5 go on sale on August 21.
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