Find Min Date based on criteria

Hi,

I have searched the web for 30 min banging my head against the wall trying to get various formulas to work for this. I included a file to explain my problem.

On the Min Formula tab I have 5 green cells where I need a formula to look at the fruit on the data tab and bring back the minimum date (earliest date) that is in a column far off to the left.


Can someone help me with this?