while i feel for your situation im kinda suprised that your suprised in any way..
You checked a 5k camera with AA with no insurance ??
Where have you been that last 10 years ?

they show videos all the time of airline employees stealing shit.. not sure why you ever trusted them to begin with..
ok now how to get your money back.. someone mentioned the grammar in your fax and you downplayed it , but i gotta say he has a point.. I have a few other tips for you as well. Consider your fax as a $5000 fax so its really important its done well.. Companies dont care about you , they care about $$$ thats it.. they dont care about your loyalty etc.. So get down to brass tacks, and make them see how much $$ they will lose if they ignore you..
example.
" Dear AA , My name is John Smith and i am the owner of a hollywood film production company. My employees all fly AA business class , totalling over 100 flights a year Recently i flew on flight xxx from xxx to xxx and photography itmes were stolen from my baggage by AA employees.
Included in this letter are receipts and costs to replace the items stolen. If the items are not replaced i will be forced to cancel our business flights and switch them to a more trustworthy airline.
Below are receipts for my flight and reports i filed with the police regarding the stolen items.
John Smith CEO fpb Entertainment.