One problem related to transmission not engage has been reported for the 2005 Toyota Prius. The most recently reported issues are listed below. Please also check out the statistics and reliability analysis of the 2005 Toyota Prius based on all problems reported for the 2005 Prius.
The electronic(?) shift mechanism in the car malfunctions/does not stay engaged in temperatures approximately 28 degrees fareheit & below when car has sat idle for periods of time. The night of this incident I was returning from a business trip where my car had been sitting out in the weather for approximately 28-30 hours. The temperature this particular day was 9 degrees; however, I have had this happen in the past with temperatures ranging into the mid to upper 20's. {due to our mild winter last year I don't recall it happening much if at all-- it did however occur the winter year prior [2010-2011] and I reported it to my Toyota dealer. They looked at me and told me they were unaware of any such problem. } when I position my shift select from the center position & select either drive or reverse, the car transmission disengages upon pressing the gas. The other night I had previously mentioned I had to physically hold the drive selector in the "d"/drive position for 28 minutes before the selector remained engaged. (in past incidents I have had to hold the selector in position from 5-10 minutes- the problem seems to get worse in rlation to lower temps. Are there any other reports of such a problem?.