The short answer: challenge rating measures a monster, and you are not fighting a monster, you are fighting a party. Four or five rested characters, acting every round, focusing fire, is a machine the CR tables were never really calibrated against. The number is honest about hit points and damage. It is silent about action economy, rest schedules, and the fact that your players have read the book too.
I have stood at the edge of enough battles to know how this one goes. The DM builds a “hard” encounter by the budget, the party deletes it in two rounds, and the DM concludes the math is broken. The math is not broken so much as answering a narrower question than the one being asked of it.
The three things CR does not count
Action economy. A party of five takes five turns a round, plus bonus actions and reactions. A single CR-appropriate brute takes one. However large its numbers, it loses the arithmetic of turns: stunned once, it loses everything. This is why solo monsters collapse and why the fight your players remember as hard had eight goblins in it.
The adventuring day. The 5e classes are budgeted across six to eight encounters between long rests. Almost nobody plays that many. One fight per day means every fight meets a party at full spells and full hit points, which quietly upgrades the party by several levels. The encounter is not too easy; it is the only withdrawal from an account designed for eight.
Player knowledge and focus fire. The tables assume damage spread around and monsters played straightforwardly. Real parties drop everything on one target until it dies, and CR has no column for that.
Five fixes that work at the table
Add bodies before adding hit points. The cheapest fix is numbers. Two monsters of a lower CR are usually a better fight than one of a higher CR, and four are better still. Minions give the party something to do with area spells while the real threat works.
Split the day, or split the fight. If you cannot run six encounters, run the fight in waves: the second group arrives on round three, after the party has spent its opening. A fight that arrives in two installments taxes resources the way two encounters would.
Give the monster a schedule of its own. Lair actions, or simply something the monster does every round on initiative 20 that the party must answer: the ritual advances, the ceiling lowers, a hostage is dragged one move closer to the ledge. The party’s turns stop being free.
Spend terrain like a resource. Cover that breaks focus fire, elevation that costs movement, fog that forces choices. A CR 5 monster in a room built for it plays two ratings higher; the same monster in an empty 30-foot square is an executioner’s block, with the party holding the axe.
Let the enemy be as smart as the players. Monsters that focus fire, retreat, take hostages, and pre-cast their buffs are worth more than their listed rating. If the party fights like a unit and the monsters fight like a queue, no budget will save you.
A worked example
Take a party of five at level 5, and a young white dragon, CR 6: by the encounter budget, a hard fight. Run as written in an open cave, it acts once per round against five turns, eats a hold monster, and dies without killing anyone. The table calls it a victory lap.
Same dragon, rebuilt: the cave gets ice pillars (cover), a frozen lake (difficult terrain over deep water), and six kobold skirmishers who throw nets from ledges. On initiative 20, ice groans and a section of ceiling falls where a marked character stands. The dragon strafes with its breath, lands only to pick up a netted target, and flies its prize toward the water. Not one number on its stat block changed, and the party will talk about it for a month.
Checking the arithmetic before game night
Most of this is knowable in advance: how many actions each side takes, what the daily budget says, whether the monster is walking into a party at full strength. Keeping that arithmetic is herald’s work, and it is work my own house’s tool does as a matter of course. In Herald.ink the bestiary carries CR guidance with the monster, encounters compute their difficulty against your actual party as you assemble them, and the stat blocks a fight is built from arrive balance-checked rather than hopeful. The sample campaign has encounters mid-assembly if you want to see the arithmetic done.