Take it to a mechanic
Yrs
Use Honda ATF-Z.
I've searched the web... for 2005 Honda Odyssey, it should be changed every 30,000 miles. This can be done easily it as transmission drain plug. Also, note, that there is no serviceable transmission filter; therefore not need to change. Hope this helps.
That means time to change transmission
The 2008 Honda Odyssey has a 5-speed automatic.
The 2007 Honda Odyssey has a 5-speed automatic.
The 2001 Honda Odyssey has a 4-speed automatic.
The 2012 Honda Odyssey has a 5-speed automatic.
The 2013 Honda Odyssey has a 5-speed automatic.
The 2009 Honda Odyssey has a 5-speed automatic.
The 2005 Honda Odyssey has a 5-speed automatic.