6:5 Blackjack refers to the payout for a blackjack. If you bet $5 you will receive $6 if you have blackjack. Most tables pay out 3:2. This means if you bet $5 your payout will be $7.50.
6:5 is most common for single deck games but some casinos are using it for regular, multi deck, shoes.
It increases the house advantage about 1.5%.
I remember the days when the blackjack payout was 2:1.