Interstate 865 is a short connector between Interstate 465's northwestern corner, and Interstate 65's northwestern continuation out of Indianapolis. Interstate 465 is the beltway around Indianapolis, but Interstate 65's northwest leg lies west of the beltway's northwest corner. Interstate 865 is a four-mile freeway shortcut between that northwest leg of Interstate 65 to Chicago, and that northwest corner of Interstate 465. The overall northwest-southeast alignment of US Route 52 uses Interstate 865, running concurrently with Interstate 865 for the freeway's entire length. If you're trying to get from Chicago to points east and southeast of Indianapolis, you'll want to use the Interstate 865 exit off of Interstate 65 to reach the northern part of Interstate 465. Then, Interstate 465 can bring you to Interstate 70 or 74 east away to points east, like Dayton, Columbus, or Cincinnati. Of course, people traveling in the reverse motion can do the reverse of this, too. Interstate 865 was also labeled Interstate 465 until about twenty years ago, making Interstate 465's former routing the shape of a strange, sideways "P" (or backwards lowercase sigma). I personally am glad they changed the northwestern appendage off of the loop to the new designation of Interstate 465. The interchange (exit 25) at the northwest corner of the beltway had ramps to Interstate 465 east, Interstate 465 south, or Interstate 465 west; that was just plain confusing.
Interstate 865's exit numbers increase from west to east, as is customary for east-west highways; however, Interstate 865 has no intermediate exits between its two endpoints.
The western end isn't marked with an exit number at all, actually, as westbound traffic is all routed onto Interstate 65 north toward Chicago. In the opposite direction, only southbound traffic coming from Chicago on Interstate 65 can access Interstate 865. Here's a photo of the first eastbound trailblazer, on the flyover ramp from Interstate 65 to the eastbound beginning of Interstate 865:
At the eastern end of Interstate 865, traffic is given the option to divert southward onto Interstate 465's western leg, or to continue straight east onto Interstate 465's northern leg.