Wash apricots, raisins, figs, and prunes quickly but thoroughly in cold water.
Dry on absorbent paper.
Remove pits from prunes and dates and put all fruit through a food grinder.
Turn fruit into a bowl and add lemon juice and honey, mixing well.
Cover tightly and place fruit in refrigerator for a day or two for fruit to soften and flavors to blend.
Serve in chilled sherbets with plain or whipped cream.