Despite being the fifth entry into the series, Persona 5 is the best starting point for any newcomers.
Part of this comes from dropping the Shin Megami Tensei title. Because Persona is a spin off of that franchise, previous entries have included it in the title, with Persona being more of a subtitle than anything else. Persona 5 feels like it has its own identity because of this, and it makes it much easier to jump into for those unfamiliar to the franchise.
P5 also goes the extra mile in explaining the different elements and themes of Persona. Everything, from the summon-able Persona entities that do battle to the Velvet Room is explained to the player but it leaves plenty to the imagination in case you want to figure everything out for yourself. There's also the fact that it's on current hardware, rather than the PS2 or Vita like Persona 4.
Persona 5 takes the best of both worlds by catering to a loyal audience whilst also making room for brand new fans.