Pre-heat the oven to 350°F.
In the bowl of an electric mixer, cream butter and sugars until lighter in color and well blended.
Add lime zest; mix well; scrape down the bowl to make sure all ingredients are mixed well.
Using a small bowl, add the eggs and mix until well combined.
To the eggs, add the vanilla and blend thoroughly.
In a separate bowl, sift together flour, baking soda, baking powder and salt.
With the electric mixer on low, add the flour mixture to the wet mixture; just mix until it all comes together.
Remove bowl from the mixer and hand stir in the chocolate, pistachios, coconut and dried cherries.
Using an ice cream scoop, scoop out balls of dough about 1-1/4-inches in diameter.
Place on a parchment paper lined cookie sheet about 1-1/2-inches apart.
Place in the pre-heated oven and bake for 10 to 12 minutes; turning at 5 minutes.
Since ovens can be slightly different, check the cookies at 10 minutes.
The cookies should be golden brown.
Remove from the oven; allow the cookies to rest for 10 minutes before removing from the baking sheet to a cookie rack to cool completely.
Store in an airtight container once completely cooled.