Bear with me here. While this is all purely speculation, there is some past historical evidence that would suggest that this information might be correct.
In Japan, the Persona series have their own magazines. These magazines have historically come out in the same months that corresponding Persona games launched as well.
For example, the Spring issue of the magazine released four days after PQ came out in Japan. The September issue released on the day Persona 4 Arena Ultimax. This year's July issue came out when the Persona 4 Dancing All Night.
A rought translation of the picture below states: Next Persona Magazine issue in Winter 2015 (may subject to change)
What we could deduce from this is that Persona 5 is slated to have a Winter release date in December.
Also, P Studio, the development team behind Persona, is known to announce release dates four months prior to a game's release date, which means we could officially hear about the game's release date some time in August.
