Small Axe, directed by Steve McQueen (Hunger, Shame, 12 Years a Slave, Widows), is a new, five-part Amazon series that’s meant to be seen as five full movies about the West Indian community in Great Britain in the 1960s, ’70s, and ’80s. It reflects McQueen’s own experiences growing up in London as the son of a Trinidadian mother and a Grenadian father. The first entry, “Mangrove,” is pretty damn good and promises admirable things to come in the rest of the series.

I went into “Mangrove” cold, having read nothing about it, and was a little uncertain about how to take it at first. It’s gorgeous-looking and with a great reggae score — the title of the series is taken from a Caribbean proverb that inspired the Bob Marley and the Wailers song, “Small Axe,” featuring the line, “If you are the big tree, we are the small axe, ready to cut you down.”

But “Mangrove” takes a while to become propulsive, immersed as it is in extraordinary period and cultural detail. It’s about a man named Frank Crichlow (brilliantly played by Shaun Parkes) who opens a Trinidadian all-night restaurant and cafe in the Notting Hill section of 1968 London called the Mangrove. Crichlow has had a rough history — his last place, the Rio, got him no end of police harassment and was shut down for illegal activities such as gambling and drug-taking on the premises. So he doesn’t want any trouble this time; he just wants to run his little restaurant which provides nothing but spicy food for those who like it.