I'm reading up on the lore of Forgotten Realms and wondering when in-universe 5E takes place, since my character is from Mulhorand and I want to know if The Spellplague has taken place yet, for his backstory.
Broadly speaking, Wizards keeps the clock moving forward in the Forgotten Realms, and doesn't generally release adventures and other content that happened chronologically in the past from previous content. The earliest D&D 5e playable content, the Tyranny of Dragons adventure series, starts in 1489 DR. The Spellplague stops being a major force in the world in about 1479 with Mystra's Return, so you can definitely have a chronologically accurate 5th edition character that has a Spellplague-related backstory.
In specific, Mulhorand is still destroyed, and you'd have to be pretty old to be a native Mulhorandi. However, Mulhorand seems to be coming back in some kind of mysterious, not-super-well-explained-yet way in the Second Sundering, so YMMV.
The first new 5e FR Organized Play season starts in 1489 DR, in the future after the Spellplague. The FR team put together a bunch of novels and content for an event called "the Sundering" which largely undid all the massive 4e FR changes - Aber and Toril split back apart, Spellplague over, etc. The Spellplague lasted only from 1385-1395 per se, but its aftereffects lasted till Mystra's return and the recreation of the Weave in 1479, leaving only some small pockets of the old effects. Hail to the new Realms, much like the old Realms.
The Sword Coast Adventurer's Guide says the Spellplague was unleashed in 1385 DR (dale reckoning). Another upheaval known as the Sundering occurred a century later, and is also treated as in the past (ending somewhere around 1489 DR). I couldn't find the current year in the book, but for a character in Toril's 'present' the Spellplague should be old news.