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I-175 and I-375 were planned as "downtown feeders", intended to stem further decline of downtown St. Petersburg by providing quick access to the interstate system. (The city has since rebounded, mainly from tourism.)
Both were conceived as state routes originally. However, when a funding issue led the state to cancel part of I-75 in Hillsborough County, five miles of eligible interstate were released. This opportunity led to the designation of I-175 and I-375. 
I-175 opened on April 23, 1980, at a cost of $5.5 million: at the time, the most expensive highway per mile built in Florida. I-375 was completed in early 1979. 
I-175 (cancelled) Georgia
Proposed roughly along present-day GA 300 from I-75 to Albany. It got on the federal books between 1971 and 1978, but was never built. 
I-175 (proposed) Kentucky; Tennessee
This proposed highway would shorten travel time between Lexington, Ky. and Chattanooga, Tenn. The shortest distance between those two points is not I-75 itself, which runs diagonally between Chattanooga and Knoxville. Still, Interstate 175 would be about 250 miles long.
Don't hold your breath for this one: it would be expensive to build, and so far only Kentucky has shown recent interest in studying the route. If not for an eagle-eyed fellow roadgeek poring over a federal transportation bill, we might not have even found out about it yet.
How I-175 was discovered
The first public evidence of the route, in late June 2001, was just a terse line item in the U.S fiscal year 2002 transportation bill: "I-175 feasibility and planning study, Kentucky - $2.4 m." 
Jeffrey Coleman Carlyle asked the Kentucky Transportation Cabinet (KYTC) about this, and in late July got the following reply (summarized): the idea for the road has been around for a long time: a straighter freeway or expressway route from Lexington to Chattanooga, connecting to I-75 at each end. The high cost of the route (estimated at about $3 billion) is one reason the plan has not been pursued. The money provided by Congress will only fund a feasibility study: a more thorough investigation of whether the road should be built. 
The true roadgeek's dilemma: do you advocate a new highway that, if connected to I-75 at both ends, would be numbered incorrectly? (Such a highway should start with an even digit.)
See also: Future Interstate 175 (Jeffrey Coleman Carlyle)