For a pop series in which coveting treasure invariably leads to certain doom, the prospect of a fifth and supposedly final Indiana Jones movie – with a now 80-year-old Harrison Ford in the lead, and without Steven Spielberg behind the camera – may well constitute one cliffhanger too many; a last lunge for the Holy Grail that brings the whole temple crashing down.

Forty-two years after Raiders of the Lost Ark, the series has become as nostalgic for its own blockbuster heyday as its creator George Lucas once was for the serialised adventures of his childhood; the original film’s seat-of-its-pants charm, roguish one-upmanship and spooky practical effects are now as talismanic as ancient relics.

It also means the franchise, now under the aegis of Disney, has backed itself into something of a creative corner.

Having tangled with atomic-age aliens in Spielberg’s flawed-but-fascinating Indiana Jones and the Kingdom of the Crystal Skull (2008), our globe-trotting hero is back to doing what his current minders, at least, think he does best: punching Nazis. As the traitorous American villain once sneered at Indy, in 1989’s cheerfully self-reflexive Raiders redux, Indiana Jones and the Last Crusade: “The Nazis? Is that the limit of your vision?”

Directed by James Mangold (Ford v Ferrari; Logan), who has the unenviable task of stepping into Spielberg’s sneakers (Spielberg and Lucas remain as executive producers), the Nazi-heavy Indiana Jones and the Dial of Destiny is a sincerely mounted, often gripping action movie that also runs up against the limits of its own vision.

It’s a film that wants to swing big, reckoning with an aging pulp hero out of his time, and questioning the perils of living for the past, but one whose ultimately tame execution – and, you might argue, very existence – serves to refute its thesis.

Without the playfulness of the old Paramount logo dissolve, the movie begins in gloomy media res, with Indy – played by a digitally de-aged Ford – deep behind German lines in 1944, just as the tide of the war is turning against the Nazis. He and his stuffy archaeologist colleague, Basil Shaw (Toby Jones), are trying to stop a train full of antiquities bound for Berlin (seems failing to nab both the Ark of the Covenant and the Holy Grail hasn’t dimmed the Führer’s enthusiasm), when they stumble upon half of the Antikythera, an ancient dial rumoured to generate fissures in time, and run afoul of a Nazi commander, Jürgen Voller (Mads Mikkelsen), determined to wield the mechanism for his own power.

“Whoever has it,” Voller threatens, “will be God.”

It’s a long, muddy-looking sequence that, like too much of the movie’s action, misses Spielberg’s spatial dynamism and visual wit. But the film gathers some steam and personality in 1969, where we meet a now 70-year-old Indy, stuck in a cluttered New York apartment and snoozing on a recliner in front of psychedelic kids’ show H.R. Pufnstuf, and about to be abruptly awoken by the downstairs neighbours blasting The Beatles. (The song: Magical Mystery Tour, of course.)

The crumpled professor is in the middle of a divorce and a thankless teaching job at Hunter College, where the bored, bubble-gum-popping students are more excited by the recent Moon landing than they are by ancient artefacts.

“Going to the Moon is like going to Reno,” Indy grumbles, with every right of a guy who’s seen extra-dimensional UFOs and Biblical phantasms.

The only person not looking to the future, it seems, is the now middle-aged Voller, who’s been biding his time as a NASA physicist on the Apollo project, but whose real dream is to get his hands on the dial and turn back time, using his advanced knowledge to help the Nazis win the war.

Luckily, Indy’s 30-something goddaughter, and Basil’s kid, the spirited, whip-smart Helena Shaw (Fleabag’s Phoebe Waller-Bridge), gets to it first. She’s soon whisked the dial away to Tangier, where she’s holding a black market antique auction alongside her teenage offsider, Teddy (a lively, if underused, Ethann Isidore).

With Indy joining them, it’s an old-fashioned, international jaunt that takes our heroes across North Africa and into Europe by land and sea, with Voller and his goons – a moustachioed American stooge (Boyd Holbrook), presumably standing in for a contemporary Proud Boy – in hot pursuit.

Powered by Mangold’s reliable craft and John Williams’s typically baroque score, it all motors along at a pretty rousing clip, from an improbable horseback chase through a subway to a knockabout, Italian Job-inspired escape in tuktuks, with bugs, eels (the film’s amusing variation on Indy’s reptile phobia) and a salty Spanish sea captain (an all-too-brief Antonio Banderas) thrown in for good measure.

The lanky, mischievous Waller-Bridge is the animating spark for much of the adventure; as the mercenary, ethically dubious Helena, she’s a ghost of Indy’s own past, and the actor brings out a lovely, cross-generational rapport with Ford that occasionally evokes his double act with Sean Connery in The Last Crusade.

Her presence also suggests a scrambled moral complexity: In an era when Indy’s old mantra, “It belongs in a museum,” carries a whiff of institutional colonialism, who’s to say Helena’s black market capitalism is any less noble a pursuit?

Dial of Destiny is at its best when it tips its fedora towards these grey areas, when Mangold’s sense of fraught American idealism – previously glimpsed in his intermittently compelling Ford v Ferrari – rises to the fore.

But while Mangold is a dependable action filmmaker with a steady command of the frame, the Indiana Jones films were never merely about great action; what he can’t quite summon is the ineffable magic that the original films possessed, that strange alchemy that resulted from the synchronicity of – and sometimes, friction between – their creators.