DIVERSITY: Meet the seemingly unfireable female firefighter.

Despite failing a required FDNY running test five times, Wendy Tapia was allowed to graduate from the Fire Academy and become a firefighter. On Dec. 2, she is taking the test for an unprecedented sixth time.

Tapia was one of only five women among 285 new firefighters who graduated from the FDNY’s Randall’s Island training academy on May 17.

The class was hailed as the most diverse group of rookies ever, all of them EMTs or paramedics seeking promotion to firefighter. She joined a group of just 35 women among the 11,000 Bravest.

But Tapia, 31, has yet to work a shift at her firehouse, ­Engine No. 316 in East Elmhurst, Queens, where she was assigned May 18.

At the end of 18 weeks of probationary training, Tapia failed to run 1¹/₂ miles in 12 minutes without gear, as required by the academy. She blamed a foot injury.

The FDNY let her graduate anyway — and gave her five more deadlines over the past six months to pass the running test.

She failed all five times, insiders said.

Normally, probationary firefighters who fail the running test at the end of academy training don’t graduate — period. They flunk out but can join the next academy class, start over and get another chance to pass the course.

Tapia’s treatment has inflamed male and female colleagues alike.

It’s almost like it’s about quotas over qualifications or something.