Unfortunately, there is a lot of misinformation out there about 5th gear pop-out (or any gear for that matter) being caused by worn syncros or some other problem with the syncros. The truth is, the synchronizer rings have absolutely nothing to do with a transmission staying in a gear or popping out of a gear. Synchronizers only function is to "spin up" the gears as the engagement hub approaches the gear. For a detailed look check out HowStuffWorks: Manual Transmissions. They have an excellent section about manual transmissions and synchronizers.

On the problem of 5th gear pop out, there are two sources of problems that can effect the "pop-out" issue. It doesn't matter if it is 5th gear or 2nd and it doesn't matter if it is a Toyota transaxle or a Renault. Gear pop-out is related to movement in the transmission. This movement can either be external or internal.

External issues can be linkage problems or mounting problems. Linkage problems are easy to diagnose and can typically be duplicated. Worn engine/transmission mounts can allow the assembly to move and cause strain on the linkages which can cause the pop-out. This is a little more difficult to find.

Internal issues are caused by a few items, but the most common one is worn bearings. The helical-cut gears used in production cars put great strain on the bearings. Helical gears are used because they run much more quietly than straight-cut gears. (However, helical gears are much more expensive to produce, so we know cost isn't the factor here.) The two shafts that are engaged with helical-cut gears are always trying to force each other apart along the axis of the shafts. This force is transferred to the bearings and then onto the case. Once the bearings begin to wear, the shafts develop a small amount of play and can then move along their axes. Since the engagement forks and their respective hubs also move in a motion along the axis of the shafts, any movement is going to effect gear engagement. The shift hubs are normally free to move along the shafts and once pushed or pulled into an engagement position they are held in place by only small "detent" springs. These springs need to apply only a minimal force to hold the hubs in place, but if the shaft was to move along its axis, such as in a "power on, power off" application, the detent springs have no chance of holding the hubs in place.