Adrian Peterson -- 5th Baby with (At Least) 4th Baby Mama

Adrian Peterson's baby count is now at 5 ... 'cause a 4th woman has surfaced who has a child with the NFL star, TMZ has learned.

This time, the baby mama is Erica Syion -- a former dancer who worked at a gentlemen's club in Dallas, TX. Erica and Adrian have a 4-year-old son together.

Sources connected to the situation tell us ... the two have a financial arrangement, in which Adrian gives Erica money to pay for the kid's schooling, as well as living expenses.

We're told the two met in Houston back in 2007 ... but their relationship has deteriorated in the past few years.

Sources tell us Adrian IS involved in the child's life -- but Erica is the primary parent, with Adrian visiting when he can.

In total, Adrian has fathered (at least) 5 children: 2 kids he referenced in a 2009 documentary ... one was 4 at the time. He didn't mention the age of the other (it's likely he was referencing his son with Erica).

Since then ... he fathered Adrian Peterson Jr. (who's 2-years-old) and a 3-month-old daughter with a waitress in Minnesota. His other son, a 2-year-old, passed away last week.

It's possible his 8-year-old and AP Jr. have the same mom -- but so far, we haven't been able to confirm.