One problem related to transmission not go into gear has been reported for the 2005 Honda Odyssey. The most recently reported issues are listed below. Please also check out the statistics and reliability analysis of the 2005 Honda Odyssey based on all problems reported for the 2005 Odyssey.
Travel at high speed iaw speed limits and traffic flow, noticed surging (like slipping) from transmission, noticed drive indicator blinking, engine revs surging with transmission surges. I hope to make nearest safe area to pull over (rest plaza less than 7 miles away) got 4 miles. Had reduced speed to relieve stress on transmission and engine. Speed continued to reduce suddenly to below 45 mph before I was able to find safe location to pull over. Transmision locked into drive position could not shift to any gear. No grinding sounds were ever heard. I was by myself but this could have happened to anyone. Could lead to death from being hit from rear by another car or truck as transmission's rapid rate of deceleration cause by its failure. Looked up blinking transmission indicator and did not find any warning or notification as to possible cause. Found out that Honda odessesy's transmission has history of catistrophic failure if not serviced every 35k (varies according to complaint). Again no wqarning of this possible event mentioned in owner's manuel. Since I bought the car used I had no knowledge of this problem or its service record. I did have it serviced shortly after buying it but again had no warning. Ironically, I'm an automotive reliability/safety manager by profession.