No, Blades and its derivatives (Band of Blades, Girl By Moonlight, Scum and Villainy, etc.) are typically referred to as their own thing, Forged in the Dark (FitD). The original inspiration for the system was PbtA, but Harper made so many changes for Blades that people found it more useful to treat it as its own thing.
Like I said to Charlaquin, Blades isn't (technically) PbtA. Charlaquin already mentioned Apocalypse World and Dungeon World; some other pretty well known PbtA games are Masks: A New Generation, Monsterhearts, Urban Shadows, The Sprawl, The Veil, Monster of the Week, and Legacy: Life Among the Ruins. Recognize any of these names?
If you don't want to spend money just yet, there are a few currently in development PbtA games with free previews. These documents are fairly light reading. They each do their own thing, but keeping track of the similarities between them can help you get a grasp on how PbtA works.
www.drivethrurpg.com
www.drivethrurpg.com
www.drivethrurpg.com
The digital version of Ironsworn is also completely free, though keep in mind it does diverge from the "core" PbtA experience in several major ways (though not enough to get cordoned off into its own thing like Blades).
www.drivethrurpg.com
Finally, if you're interested in the design philosophy of PbtA, Vincent Baker is writing a series of articles on his personal blog on how he went about designing Apocalypse World.
lumpley.games
The Basic Rules for 5e can be found as a PDF on D&D's website completely free. They're also available on D&DBeyond if you prefer the web page interface. It would be helpful to familiarize yourself with them.
The official home and digital toolset for Dungeons & Dragons. Dive into D&D books, create a character, and more!
dnd.wizards.com
This section contains the Dungeons & Dragons Basic Rules and the rules in the SRD, released as part of the Open Gaming License.
www.dndbeyond.com