Creating a syndicate to not pay rental income tax?

[Spencer Cornelia]

Quick thought: could a group of investors team up and combine their yearly net rental income into paying for a new property?

Example: a group of 5 investors each net $5k every year in rental income.  After year one, they combine their total $25k into a down payment for another property.  After year two, they combine their $30k ($5k + $1k from new property each) and buy another property.  And so on...

From what I've read, they would not be paying any income tax on the $5k they earned because of buying the new property.  And they are also expanding at a much faster pace.  Is this a dumb idea?  Why / why not?