Subway crime has dipped in the Big Apple — but try telling that to the victims of these transit terrors.

A cluster of 63 career criminals continues to wreak havoc in the city’s underground, racking up more than 5,000 busts between them — yet only five of them are currently behind bars, The Post has learned.

The motley crew has amassed a disturbing rap sheet for crimes including assault, robbery, theft, turnstile-jumping and a string of other nuisance offenses — but they largely remain free because the state’s lax criminal-justice reforms bar judges from holding them on bail. 5

“Crime is down in the subways, but it’s the same handful of criminals making it feel like chaos,” a frustrated law-enforcement source said. “This kid gloves approach to bail and lack of prosecution isn’t cutt

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