I'd try Option 2

Option 1
1. Create a custom date range:
2. Go to Reports > All Reports
3. Select the report you want to run (e.g. Sales by Product/Service)
4. Click the Customize button
5. Under Filter, select the Date option
6. Select the option for "Custom" and set the date range to start on June 1 and end on May 31 for each year.
7. Apply the filter and run the report

Option 2
1. Create a new fiscal year:
2. Go to the Gear icon in the top right corner of the QuickBooks homepage
3. Select "Fiscal year"
4. Click the "New fiscal year" button
5. In the new fiscal year form, change the start and end date according to your needs, June 1 to May 31
6. Save the new fiscal year
Now, when you run reports, you can select the new fiscal year as the date range.