Preheat the oven to 350°. On a rimmed baking sheet, toss the bread with 2 tablespoons of the oil. Bake for 15 minutes, stirring once, until lightly toasted. Let cool.
In a large bowl, whisk the mustard with the mayonnaise and vinegar. Gradually whisk in the remaining 3 tablespoons of oil and season with pepper. Add the celery, ham, cheese, chives and the rye bread croutons, toss well and serve.