well, if you will run your cards with lower setting for power limit, like 70% so it would be aprox 105-110W each
so I think if you will not outlimit those limits you will be ok even with something cheaper then 1KW - Corsair 850W will be good
That is true in terms of power consumption, but if he goes with 5 cards, he'll need 10 pci-e connectors and then 5 peripheral molex/sata cables for the risers. Not many 850W PSUs come with 10 pci-e connectors, it's usually only 1KW+ units that have enough.
VERY FEW 1070 cards need more than a single 8-pin (or 6+2 pin) PCI-E power connector.
Ditto 1070 ti cards - I'm not aware of ANY of those (so far) that need more than one connector.
1080 it's more common but a lot of them are still single connector.
That monster MSI Gaming thing with the 240 watt TDP rating is the only one I know of for sure, but there MIGHT one or more others I'm not aware of.
SATA is a VERY VERY BAD IDEA for riser usage - the connector ITSELF is only rated for 54 watts MAX (3 connectors at 1.5 amps each), the PCI-E spec calls for up to 75 watts draw out of the PCI-E BUS connector and many cards have been shown to pull a little MORE THAN THAT (specifically including some AMD RX 470/480 cards).
"MOLEX" connectors on the other hand are rated for 13 AMPS per pin used (normal computer usage is 1 x 5 VDC, 1 x 12 VDC, 2 grounds) for 156 watts rated capacity - which is PLENTY for PCI-E bus power.