According to the suit, obtained by TMZ ... the women claim the disgraced actor/comedian masqueraded as their mentor as they tried to break into show biz in the '80s and '90s, but instead he turned into a predator.

Plaintiffs Lili Bernard, Eden Tirl, Jewel Gittens, Jennifer Thompson and Cindra Ladd say Cosby was able to take advantage of them because they were young and vulnerable.

Lili guest starred as Mrs. Minifield in a 1992 'Cosby Show' episode ... and in the lawsuit, she says Cosby drugged and assaulted her several times -- including one time when she woke up during the rape to find him trying to smother her with a pillow.

According to the suit, she threatened to go to the police, and Cosby threw her down a flight of stairs and kicked her out, warning he would destroy her. She says she didn't report the alleged crimes out of fear for her life.

Eden Tirl -- who had a bit role as a cop on 'Cosby' -- alleges she was "escorted" by one of the employees on set to Cosby's dressing room, where he locked the door, grabbed her breasts, kissed her neck and pressed his penis into her back while whispering, "This is making love."

In the suit, Gittens says Cosby drugged and assaulted her at his home while they discussed a possible role for her on the show -- Thompson claims he forced her to masturbate him ... and Ladd alleges he raped her after giving her a pill for a headache that made her pass out.

As we reported, Cosby has been accused of rape by dozens of women over the years -- allegations that he denies. In 2018, he was sentenced to 10 years in a Pennsylvania prison for indecent assault -- but, he was released last year because prosecutors had violated an immunity deal Cosby had been given by a previous district attorney.

Earlier this year, he was found liable by a California jury in a civil case of sexually abusing a teenage girl in 1975.