1998 Mitsubishi Galant no fifth gear or reverse

1998 Mitsubishi Galant mileage: 60,000. I have question about transmissions. I have a Mitsubishi Galant with a semi-new engine and just about everything else has been replaced. The last thing to fix in the old car is the transmission. It has a 5-spd manual transmission. While driving on the interstate a few weeks ago, the fifth gear would "slip out" and the gearshift would go back to neutral. So to make it home, I had to hold it in fifth position. Eventually it went out completely. I got it home, but then when I wanted to move it out of my garage I could not put it in reverse. So, both the fifth gear and reverse are no long useable. I've contacted some mechanics in my town, and they say that the synchronizers are shot and that I will need a new transmission. I was just wondering what you guys think about the situation, and if you could help. Thanks a bunch!