The 5e PHB is pretty unambiguous about familiar "death". Per the find familiar spell description:
When the familiar drops to 0 hit points, it disappears, leaving behind no physical form. It reappears after you cast this spell again.
You can also use the spell to change your familiar's form.
Is this familiar, for all intents and purposes, exactly the same being you summoned before?
In other words, is familiar death in 5e just a temporary inconvenience, or does it have repercussions of some sort?
Best Answer
It's just a temporary inconvenience, except in a singular case.
Basically, all that a familiar's death means is that you'll have to recast Find Familiar at your earliest convenience (so it means the loss of a spell slot for a day if you have a time pressure and can't take the extra 10 minutes to cast it as a ritual). The spell/ritual does cost 10gp, but that's a pretty trivial amount for an adventurer. It also has a casting time of 1 hr so your party probably needs a short rest while you do it rather than simply doing it between encounters.
The only case where having a familiar come to harm is a permanent issue is in the rare event that you decided to retrain the spell (or as a wizard, have lost the spell book that contains it). These are the only times when losing a familiar has long term ramifications.
As to whether or not the newfound familiar obtained when you recast the spell is the same being reincarnated/resurrected, or a different being entirely, this is up to you and the flavor you choose for your familiar.