Call it a rebirth: Matt Damon is back as Jason Bourne in the franchise’s tough, “this time it’s personal” fifth installment, titled, simply enough, “Jason Bourne.” To the extent that the entire Bourne series hinges on the notion of an amnesiac action hero — one who remembers how to kill with his bare hands but draws blanks on key details about his past — this explosive reunion between Damon and director Paul Greengrass further reveals key secrets about Bourne’s origins, bringing its lethal protagonist as close as he’s ever likely to get to total recall.

Mostly, the project marks a return to what worked about the franchise — namely, Damon — suggesting the relief of watching Sean Connery step back into Bond’s shoes after producers tried to replace him with a suave male model in “On Her Majesty’s Secret Service.” Meanwhile, audiences are expected to forget both “The Bourne Legacy,” 2012’s disappointing attempt to carry on the name by casting Jeremy Renner in a superficially similar capacity, and “Green Zone,” the gritty (and virtually unseen) Iraq War thriller in which Damon and Greengrass tried to get serious. Now, the real Bourne has resurfaced, and both director and star are committed to making the most of it, holding us in their thrall until the Las Vegas-set finale, when this hyper-paranoid conspiracy thriller tilts into something bordering on silliness.

So, what has Bourne been doing all this time? Turns out he’s been squandering his super-soldier training on grungy underground prizefights when Nicky Parsons (Julia Stiles) shows up with a fresh reason for him to reengage with his past. The game has changed in the decade-plus since Bourne went off the grid: Technology trumps things that go boom, and shadow operatives kill with keystrokes rather than old-school tactical strikes. In this new arena, the most dangerous players aren’t foreign powers, or even terrorists, but hackers and information jockeys, à la Edward Snowden and Julian Assange.

Parsons has fallen in with a WikiLeaks-like crusader named Christian Dassault (Vinzenz Kiefer), determined to reveal the CIA’s shady dealings, which point to a plan to force its way into a Facebook-like social network called Deep Dream. Sneaking past the agency’s firewall from a warehouse in Reykjavik, Parsons manages to steal classified files with fresh information on Treadstone, the black-ops program for which Bourne was recruited, and its successor, code-named Iron Hand — information that appears to implicate Bourne’s own father (Gregg Henry) in some capacity.

But Parsons’ hack doesn’t go undetected, catching the attention of Heather Lee (Alicia Vikander), who stands in the middle of what looks like Mission Control for one of the Apollo landings — an elaborate CIA data-crunching center, where techies sit at computer consoles, presumably aggregating private information on American citizens. If the expressionless Vikander is meant to represent a newer, smarter CIA, then new addition Tommy Lee Jones, who plays agency director Robert Dewey, suggests the battle-worn and borderline-haggard version of his former Man in Black. He has dark pouches under his eyes and walks with a limp, and his good-ol’-boy drawl belies the fact that the man at the helm during an age of cyber-warfare most likely still has an AOL account.

And so Dewey delegates the high-tech duties to Lee, while depending on a contract killer known as “the Asset” (Vincent Cassel) to deal with the real problem: silencing Bourne. The sort of sociopath who never met anyone he didn’t finish by shooting directly in the forehead, Cassel’s character is just plain ruthless — and clearly a better match for Bourne’s skill set — which makes for violent efficiency as the two characters alternately stalk one another. Bourne wants to get to the bottom of the secrets involving his dad, and for that he’ll need to confront Dewey. Dealing with the Asset is sort of a bonus, yielding a reckless car chase that feels particularly insensitive in the wake of this month’s terror atrocity in Nice.

The conventional wisdom on the Bourne series has been that the Doug Liman-directed original, 2002’s “The Bourne Identity,” made for a sleek 21st-century spy movie, but that the series didn’t really kick in until Greengrass came along and shook things up with his two sequels, “The Bourne Supremacy” and “The Bourne Ultimatum.” Revisit all three today, however, and it’s the first installment that holds up best, setting the tone for all that follows: While Greengrass was rightly praised for the intensity of his vérité style, with its dizzying handheld camerawork and splintered editing, it was Liman, operating from the sturdiest script of the bunch, who established a tougher, more “realistic” style of acting — and action — and who pressured the studio to let him shoot on real European locations at a time when other action movies cut corners.

Still, there’s no question that Greengrass took those innovations and ran with them, and his typically jittery style has had such an influence on the genre that “Jason Bourne” feels like less of a sensory assault without sacrificing an ounce of excitement. Frustrated that earlier Bourne movies started shooting before the script was finished, Greengrass co-wrote the new film himself, partnering with longtime editor Christopher Rouse to deliver the series’ most globe-trotting installment. The action skips from Iceland to Berlin to London to Washington, D.C., taking a stunning detour through a massive, impressively staged protest in Greece.

In many ways, “Jason Bourne” is the most unsettling movie in the series, seeing as it points to a vast conspiracy directed at the American people, and Greengrass’ style — rendered visceral via the marriage of Barry Ackroyd’s on-the-fly lensing, a tense techno score, and Rouse’s cutting-room trickery — lends itself nicely to an era in which shadow forces rely on such tools as satellite surveillance and facial-recognition software. In one scene reminiscent of Alex Gibney’s recent “Zero Days” documentary, Vikander’s Lee hacks the Reykjavik power grid. In another, she wipes a laptop by tapping into the nearest cell phone.

It’s odd then that the instant the movie hits the Exocon convention in Vegas, where the potential for high-tech malfeasance ought to hit an all-time high, the film’s energy flags. Greengrass serves up long sequences of characters opening and closing doors, walking down corridors, trading text messages, and so on — all actions of a sort, but not the kind that make for a lively action movie — until the shooting starts. Just as the initial Damon-driven trilogy wrapped up Bourne’s business but left us wanting more, this sequel offers closure even as it entices us with the possibility of his return.