Date range search and marking if theres a value

I am looking for the correct excel formula for the following problem:
- in the corresponding cell - marked in yellow in the image - you should mark with an x if there is a value in the given row (letter I on a green background) and that value falls within the date range marked in rows 5 and 6. It does not matter how many real values - green letter I - are in the given date range, just one is enough to be marked in the yellow column.

Thank you very much in advance for your help!
Tom