Hello and welcome.
Port 7000 is used by some gaming websites, BitTorrent software, and sometimes other file sharing services. Also, it can be used by Macs for AirPlay.
-Which version of OS X?
-Do you have an Apple TV or other AirPlay-enabled devices?
-Do you have any BitTorrent software installed?
-Do you have file sharing enabled?
-Do you have Little Snitch installed and is that where you are seeing the attempts?
C