No, he's right. There are 5 cores, but it's only a "quad core" chip, with a companion core being activated for low-end tasks (while deactivating the other 4).
So it's very similar to Samsung's Exynos 5 Octa, although I have serious doubts that the low-clocked A15 is more energy efficient than a quad core A7.
If OS supports the multi processing mode of big.LITTLE technology, then yes, APP can access all eight cores.
big.LITTLE supports three operation modes. Cluster migration, CPU migration, and multi processing mode. In multi processing mode, all four A7 cores and four A15 cores are on at any time.
SAMSUNG's new exynos chip also supports all of those three modes.
Check out the ARM website.
This is Quad Core SoC, not Eight Core. In Peak performance mode, it will be only Quad A15 running. A7 only kicks in at low power mode to replace shutting down A15. Nvidia Tegra 4 claims to be Quad Core SoC but I am sure there is similar Big-Little arrangement to have 4 Low Power Cores behind.
Looking at http://www.phoronix.com/scan.php?page=article&item=samsung_exynos5_dual&num=1 a 4 core A15 SoC provides sufficient compute power even for more than 80% of all commercial desktop needs. Future will be interesting ...