In OE, when you do a shipment/invoice, the Totals tab has the Invoice Date. This is the date that is used for the IC Historical Transaction. It doesn't matter what date you use to sign into OE nor the date that you run Day End.

To see the 'ins and outs' of the item quantity, try previewing the Stock Card report in Inventory. This can be found under the Reports menu and the Stock Control section. This report calculates the qty on hand as of a past date in the same manner as the Item Valuation report, and you can see the 'running progress' of the quantity, within each location. In your case, use a date range of Dec 1 to 5 and hopefully you should see the correct Opening Qty and all the transactions you posted for that item.