I believe the info you are looking for can be pulled from the 'TESTCYCL' table. In this table, you will find the following info - Test Set ID, Test ID, Test Order, Status, Tester Name, Execution Date, Execution Time, and the Version Stamp, which give you the number of times that test has been executed. First, you will need to make sure that the ENABLE_CREATE_LEGACY_EXCEL_REPORT parameter has been added in Site Admin if you are using a version of ALM 12.0 and newer. Next, you will need to access the Analysis View module. In the Analysis View module, click the drop down on the green plus button and select 'New Excel Report'. After you have named the excel report, enter the SQL query posted below into the Query1 text box and click 'Generate'. Select a save location for the excel report, click Save, and the excel report will open. If for some reason it doesn't open automatically, you can open from where it was saved.
The query below displays all tests executed between a specified time period. You will need to edit the dates in the query to meet your specific needs.
SELECT * FROM TESTCYCL WHERE TC_EXEC_DATE BETWEEN 'YYYY-MM-DD 00:00:00' AND 'YYYY-MM-DD 00:00:00'