Presumably, you bought the '05 as a car that you had long term plans for. Hopefully you have a budget for some pretty expensive things that the car may require, including repair or replacement or conversion of the transmission to manual.
If I were in your situation, and was willing to put the needed $ into it, I would find a trusted mechanic very familiar with these cars and then have the mechanic do all of the following at the same time: 1) the timing belt, water pump and probably motor mounts, and while at it, see if the original balance shaft module is still there and if so delete it (no better time to do that, new oil pump etc etc), and 2) convert the transmission to manual.
At this point in time, there are probably very few '04-'05 Passats out there with less than 125-150,000 miles on them with a transmission you can just grab and unless a used transmission has been serviced properly over that period, replacing your transmission with a used donor transmission from a parts car or junkyard donor is probably living on borrowed time or too risky to even bother with. Price out the difference between a manual conversion and $ to purchase and install a remanufactured transmission before you make a decision to go with used or remanufactured one.
If you do all the above and car is in great condition otherwise you have great vehicle that may last a long time and be fun to drive, and fuel efficient. If spending $4-$6,000 to making this transition is too much for you, I would sell the car and find a better one.
