Pour vegetable broth into a pot and bring to a boil.
Heat oil in a skillet over medium heat; cook and stir onion and celery in hot oil until tender, 5 to 10 minutes. Add Chinese 5-spice powder to onion mixture, stir to coat, and cook until fragrant, about 1 minute.
Mix sweet potatoes, apples, salt, and onion mixture into broth; cook until sweet potatoes are tender, 20 to 25 minutes. Cool soup for at least 5 minutes.
Pour soup into a blender no more than half full. Cover and hold lid down; pulse a few times before leaving on to blend. Puree in batches until smooth.