AN5812 is a mil-spec standard for an aircraft pitot tube.  How can I
get a copy of the detailed specifications for AN5812?

Hello bencooper, I tried to find AN5812 for you free, but failed. Here
is where you can either download or get a hardcopy of the entire
document:

http://global.ihs.com/doc_detail.cfm?currency_code=USD&customer_id=21254D36380A&shopping_cart_id=2825583F2F49503C4E5A3D20290A&rid=IHS&input_doc_number=AN5812%20&country_code=US&lang_code=ENGL&item_s_key=00006486&item_key_date=120925&input_doc_number=AN5812%20&input_doc_title=

AN 5812 - Complete Document  
Revision: 7    Chg: CN1    Date: 06/03/96    
TUBE, PITOT ELECTRICALLY HEATED, "L" SHAPED  

 
Document may be cross-referenced, superseded or canceled 
(See Comments and Superseding Document below) 

Comments:   CNCL NO S/S   
Superseding Document:      
Page Count:   3   
In Stock:   Yes   
Hardcopy Price:   $ 25.00     
Download Price:   $ 25.00

Sorry I couldn't get it for you free, but I guess $25 isn't too bad if
you really need it.

Good luck, Redhoss