Well, now you guys made me do it, I had to go figure out how many monsters are currently in 5e, just to work out what we would need for books/cards for this edition alone. D&D Beyond's filters are both helpful and, annoyingly, not helpful in this endeavor.
Currently, there are 2753 statblocks listed on their Monsters tab. However, a lot of them, 285 to be exact, are duplicate legacy entries, mainly from VGtM and MToF ( I didn't include the 5 orc stat blocks from Volo's that weren't reprinted in MotM and thus weren't duplicated.); the fact that there is no "Legacy" sort option made this a pain. There are, if I counted correctly, 225 named humanoid NPCs who, according to various definitions, may or may not count as "monsters" (the NPC tag is very inconsistent in D&DB, pulling in legacy stuff and just random things. Who put an "NPC" tag on Animated Statues?). So, there are (if did my counting and math right) 2468 or 2243 monster stat blocks in 5e currently, depending if you count individual humanoid NPCs or not.