In large bowl, combine cauliflower, red pepper, carrot, celery, and olives.
In nonreactive 4-quart saucepan, combine sugar, vinegar, water, and salt; heat to boiling over high heat, stirring occasionally.
Reduce heat to low.
In container with lid and large enough to hold vegetables, place mustard seeds and crushed red pepper; pack vegetables into container and pour hot brine over, making sure vegetables are completely covered with brine.
Allow giardiniera to cool, then chill for 3 hours before serving.
Refrigerate pickles in an airtight container for up to 1 week.