The Biggest Change will be to the Necromancer's Spellcasting
If your party was even a single level higher, it probably wouldn't be a concern, but at level 5, lacking the Paladin's Aura of Protection feature, spells like Circle of Death (8d6→28avg), Cloudkill (5d8→22avg), or Blight (8d8→36avg) could be instant kills against your party. Especially if the Paladin goes down, since they're your primary healing for the party.
My recommendation is that you scale them back to being a 7th level spellcaster, instead of a 12th level spellcaster. This means dropping the 5th and 6th level spells completely, and only giving them a single slot for their 4th level spells. You might consider dropping Blight as well, though if you only target the Barbarian with the spell, its damage will be severely reduced, so perhaps it will be less of an issue. Blight would have a strong ability to OHK your Wizard though, so be very careful with how that spell gets used. You'll also want to scale back their overall spellcasting modifier from +7 to +5, also scaling the DC for their spells from 15 to 13. Lower their Intelligence score to 15 to accommodate this change. They should also see reductions to their Saving Throws to +5 for Intelligence, and +4 for Wisdom. The normal version of the Necromancer deals 3d8(13) damage with the Chill Touch cantrip, that should be scaled down to 2d8(9).
You don't want to reduce the HP total too much, since your Oathbreaker Paladin will be fully capable of dealing 20-40 damage in a single round, depending on how well they roll. Maybe consider dropping it to 50-55 health, instead of 66 health.
The outcome of the fight will then depend on how well your party manages their health pools. Liberal use of spells like Chill Touch could drop PCs with little chance of recovery, since it blocks healing when used. Your Paladin will be a decent healer, but at only 6 spell slots and 25 points of Lay on Hands, they're going to be limited to healing up an average of 79 (4x(1d8+3) + 2x(2d8+3) + 25) hitpoints worth of damage, which will go down if they use their spell slots on literally anything else, or if the Necromancer persistently targets someone with Chill Touch. If the Wizard or Paladin have already used up some of their resources for the day before this encounter begins, this encounter could be very deadly, even with these adjustments.
Spells like Animate Dead could make the fight very difficult for the PCs, but your Oathbreaker paladin does have their Control Undead Channel Divinity feature, which could also swing things in their favor in a big way, depending on the environment they're fighting in. Blindness/Deafness could cripple your party, and spells like Vampiric Touch or False Life could cause the encounter to last a long time, burning off valuable Paladin resources for healing.
Keep an eye on your party's vital stats. If you don't want this to be a deadly encounter, and it seems like the party is on their last ropes, maybe retcon the Necromancer's health until a single hit is enough to bring them down. Fights with spellcasters tend to be a bit swingy, so just gauge the encounter as it plays out.