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Frulam Mondath is a level 5 spellcaster. She exclusively uses cleric spells, uses wisdom as her spell modifier, and is connected to a site that contains a shrine to Tiamat. It is very clear she is intended to be a level 5 cleric of Tiamat, but 5e refuses to state that outright.
I don't have a solution to offer, but I do share your frustration.
Long argument in favor of CR.
Non-spellcasting classes are trickier, and not at all obvious. For example, an Assassin deals 4d6 sneak attack damage and has evasion, which would suggest a 7th or 8th-level rogue, but also has multiattack, which would suggest a 5th-level in some other martial class. Since they have 12d8 hit points, it's probably 7th level rogue with the Assassin subclass and 5th level something that's not a fighter, monk or ranger, but gives them a second attack, crazy poison damage with their weapons and nothing else.
It gets even more complicated with the "special" NPCs that have their own stat blocks in the adventures, like Severin for example.
Moreover, the way CR is calibrated in 5th edition doesn't provide a simple solution like "multiply CR by 4 and then you get the effective level", and some NPCs are harder to draw parallels than others. Maybe the number of hit dice is a better indication of level, but the rest of the stats generally don't unequivocally determine the class (which is probably by design to provide some suspense, like legendary actions).
In summary, I don't think it is possible to have a catch-all class-equivalence algorithm for 5th edition NPCs, so a parallel with previous editions may not always be possible. I see two alternatives:
- state the class when it's obvious (like the archmage) and keep the NPC name when it's not (like the assassin), which may lead to disagreements on interpretation;
- keep the NPC class in all cases and use CR instead of level in the 5e block.
I'm in favor of the second alternative, mostly because it keeps with the official content and provides a clean solution, despite sacrificing the comparison with previous editions.