Here is what I would try (although no guarantee here).
Print out the following form:
Check that it was a registered mail item. At the top of the second page, follow the directions listed for the registered mail items.
You'll also need to show the item's value or estimated repair costs, with sales receipts or invoices (send in copies - do not send originals and ensure you still have them).
Be sure to keep all of the materials together that you received as you may be required to bring them in once your issue is looked at (to your local post office).
Mail those materials along with a second sheet that you need to complete (would type it out) that explains the situation and what occurred. Be as informative and descriptive as possible so that they will have that additional information when they consider your claim.
Without the insurance, it is not definite that you will be able to recover money on this. However, over the years, I have seen people who were successful by completing this method and including written explanation and proof of value of items.
USPS Domestic Claims
PO Box 80143
St Louis, MONNN-NN-NNNN/p>
Since you used registered mail, you will not be able to file Online.
I wish you all the best! Good luck and I truly hope you are able to be successful in this regard.
It will take about 30 days to get a response and resolution one way or the other.
In my professional experience, I think you will want to mail in this information along with your explanation as yours is such a high value of loss. If it was $500 or under, I would go ahead with the Online, but you are out almost $5000 and I think that the more explanation that you can provide along with the copies of the value of your items, you will be a step up in the process and have a better chance in this situation. This is especially true since you did not have insurance on the item (that would work better for the Online method).