Finding an apartment in Manhattan is getting even harder, as listings plummet and rents reach $5,000

A new report shows Manhattan rents up and inventory down. deberarr/Getty Images A new report found that the median rent for a Manhattan apartment is $5,000 a month and climbing. Inventory has fallen as New Yorkers can't afford to move. Mayor Zohran Mamdani has pledged 200,000 new homes in NYC, but it's a lofty goal. Renting a New York City apartment isn't for the weak. The median Manhattan rental price for a market-rate apartment soared to $5,000 in July — up 3% from June and 6% from July…