Pulling a lot of mobs for leveling is a rather bad idea when playing solo as a cloth class. You are too squishy to effectively tank 5+ enemies without cooldown usage.
Now while I'd recommend you to pull single mobs when leveling, you can still try to grind your way up to level 100 by killing multiple NPCs at the same time but there are some things you should keep in mind.
An important thing to note is that the talents for leveling are different. While you would usually pick up Insanity as your level 45 talent in a raid, you should pick Surge of Darkness when you are soloing quests etc. Mainly because of the extra burst you'll get.
Something that also should be mentioned is Crowd Control. Yes I know. Priests aren't hunters with 30 traps and slows but you should make use of the spells you've got. Try to Fear enemies who get too close with Psychic Scream while also kiting dangerous melee mobs. Basically just try to avoid as much damage as possible.
Single vs. Multitarget
While leveling you should generally focus on singletarget damage. Even if you're pulling a lot of NPCs it's usually better to focus them down one by one instead of trying an AOE rotation. (I acutally think Tank roles and DPS warriors are the only classes that can really pull 10 NPCs or more while still clearing them quickly without dying). The shadow priest has some nice burst potential. You can usually kill a NPC with
Mind blast -> Shadow Word: Pain -> Mind Flay -> Shadow Word: Death
While of course looking out for procs which allow for even more burst. (Vampiric touch isn't really too good while leveling)
If you're fighting a lot of enemies you can multidot with your Shadow Word Pain but you should still have one focus target. Also always use your Devouring Plague on cooldown.
(Defensive) Cooldowns and Selfheal
Every class has Cooldowns and a SP even has quite a lot of healing potential. Don't hesitate to use your CDs. 5 minutes recharge time aren't a lot while leveling. Especially not if it lets you kill stuff faster. Use Offensive and Defensive cooldowns as often as possible. If you're taking too much damage, use your dispersion and run away or Shield yourself. If you're low on health CC the enemies and start healing yourself.
If you follow these steps you won't die that often. But remember everyone can die while leveling. You can accidentally pull too many NPCs or ignore a certain mechanic that an enemy has. Cloth classes just aren't made for tanking a lot of NPCs.