Cohen and her colleagues hope revenue from the fee will help to reduce the time it takes police laboratories to analyse "rape kits", the name given to packets containing hair, blood and other samples that may contain DNA evidence which are routinely taken from victims of sex crimes.
Houston lacks the funds to properly support crime labs, and has a backlog of 6000 unprocessed rape kits.
The "pole tax" will generate around US$3 million each year, supporters estimate.
The fee also applies to bars and nightclubs which offer one-off events that could be construed as sexually explicit, such as wet T-shirt contests or "naked sushi contests", in which revellers are invited to eat raw fish off the body of a nude woman.
The patrons of Houston's strip-clubs now face a double-whammy: in addition to the city's tax, they already have to pay a US$5 fee to the state of Texas when visiting an adult venue, thanks to a law passed in 2007.
That fee was recently upheld by the state Supreme Court, after exotic dancers filed a lawsuit claiming it violated free speech rights.
The adult industry is lobbying hard against the new fee, arguing that it represents an unnecessary burden on job-creating businesses at a time of economic strife. Albert Van Huff, a Houston lawyer who represents strip clubs, told the Journal the tax was based on flawed logic.
"There is no known correlation between people going to nice, high-end gentlemen's clubs and rape," he said.
But Jack Christie, a councillor who voted for the levy, said he doubted it would destroy the strip clubs.
"When you look at videos and see women putting $5, $10 and $20 bills in their remaining clothing, I don't think a $5 tax will hurt anybody."
- Independent