If the original three films incorporated elements of 30s - 40s movie genres and and KOTCS drew from late 40s - 50s movie genres, what could a 60s set Indy V draw from while still remaining true to IJ?
Also, while the first four films featured elements of the eras they were set in (Nazis, Anything Goes, the Gerswin song in LC, rock in KOTCS), what would you be okay with being featured in Indy V from the 60s?
Location: Tannhäuser Gate, former resident of Tanis.
The early 1960s (before the Woodstock era) was marked a lot by the post-colonial confusion caused by the collapse of the imperial system across the globe. If Indy travels to certain locales (such as most of Africa and Asia and certain Caribbean nations), the world events going on at the time could add some interesting tension to his journey, as well as exotic set-pieces for him to venture to. As a bonus, both the Soviets and the Americans were heavily interfering with these newly-freed nations at the time, so it would give Indy an opportunity to deal with some nefarious spy-types, which would give the film a pretty authentic sixties feel.
In terms of genre, the first James Bond movies were in the 60s, and since Raiders was done as Spielberg's version of a James Bond movie, I could see Spielberg looking in that direction for inspiration now.
As for mythology, Edgar Cayce predicted Atlantis would rise in the 1960s, so that could be incorporated into the plot.