It has been a long, bumpy road to the realization of a fifth Indiana Jones movie, to the point where I wouldn't be so confident that road leads anywhere but over a sheer cliff. Still, anything on Lucasfilm's slate that isn't Star Wars is enjoyable to cover, so I'm always game to pounce on the latest rumors.
Those come from The DisInsider, who claim that Disney has booked Pinewood Studios for an August 2021 production start date. Even if this is legit, it proves little, as soundstage bookings can easily change, but the timetable does shake hands with precedent: Crystal Skull began shooting in June 2007 for a May 2008 release. The new film is slated for July 2022.
It's probably as late a start date as the project could get away with given that release date, though I'm sure that's by design. Optimistically, the worst of COVID-19 will be behind us next summer, and that's no minor concern when you've got an ambitious, globe-trotting shoot* carried on the shoulders of a 79-year old.
Speaking of optimism, it has recently been confirmed that James Mangold's regular DP Phedon Papamichael will be shooting the film. This is perhaps the one silver lining of Spielberg stepping down as director, as it permits one to hope that the movie won't be patterning its visual identity after Sky Captain this time out.
*At least, if they're making the movie correctly it will be. No more Indy installments shot on Los Angeles soundstages, thank you kindly.