For all its slam-bang adventure, the new “Pirates of the Caribbean” is a very timid movie. It’s got sensational stunts, epic scope, baroque set design and superb special effects, but not much wind in its sails.

This episode feels like the fourth film in a trilogy, wheezing along when it should leap, relying on our affection for recurring characters rather than taking us on a bold new journey of discovery.

There’s a chase or brawl or sword fight every couple of minutes, but those knockabout scenes don’t infuse the movie with the headlong momentum of the earlier entries. The rambunctious brawling feels like a nervous urge to keep the frame active.

The actors know this is supposed to be a spoofy slapstick farce, but director Rob Marshall (“Chicago”), stepping in for original helmsman Gore Verbinski, seems to have lost the map to the buried treasure. Instead, he’s taking his cues from the Official Summer Blockbuster Franchise Playbook. When in doubt, toss in an action sequence.

The marquee attraction, of course, is Johnny Depp as Capt. Jack Sparrow, and audiences will forgive the film almost anything for a glimpse of his gold-toothed grin. Depp still radiates verve and prankish humor.

In an early London scene, Jack is dragged in chains before King George II and remains unflappable in His Majesty’s presence. He improvises an elaborate escape from the palace involving a napkin, a chandelier, a pastry, a passing coach, a society woman’s pilfered earring and a flaming coal wagon.

The bedlam is competently staged, but it’s Depp’s pixilated bravado that truly sells it. His Jack is such an inspired, amusing opportunist that his antics inspire almost immoral delight.

The royal audience eats up several minutes with chatter about England’s race to locate Ponce de Leon’s Fountain of Youth before the rival Spanish can claim it.

Which brings us to the main course of the story, the race to locate the fountain. Jack’s old nemesis Barbossa (Geoffrey Rush, his drawling pirate inflections stroking each line of dialogue like a kitten), has given up piracy to become a privateer for the king.

Angelica (Penelope Cruz), a spitfire old love of Jack’s, is in league with Blackbeard (the casting agent’s go-to bad man, Ian McShane), a fearsome pirate and master of impressive supernatural powers.

The race for the prize ought to lend the story an irresistible drive, yet for long stretches the film seems to be sailing around in circles as unnecessary characters and gimmicks are introduced.

This chapter drops sappy lovebirds Orlando Bloom and Keira Knightley, but drags in wimpish Sam Claffin and Astrid Berges-Frisbey as a preachy young missionary and his beloved mermaid. Yes, you read that right.

With all these associates and relations and new-character narrative ballast on board, the story tootles along like a tugboat.

The story has such a thrown-together quality that I spent more time puzzled than thrilled. Logic isn’t just broken, it’s smashed. Didn’t Barbossa die in the last episode? Why does Blackbeard stop using his sorcery just when the fountain is within his grasp? Why didn’t someone lock the screenwriters in a room until they came up with better verbal duels between Depp and Cruz?

I admire Depp’s finesse, and Rush is a treat, but there’s only so much that fresh performances can do to liven up lackadaisical material. The film smells of dead fish, yet the now-mandatory post-credits scene seems to pave the way for a second trilogy. Didn’t anyone learn from “The Phantom Menace”?