Take a real close look at the track for the "L" shift fork's dog (the dowel that moves it around). If the tip of the Neutral peak on that track is chipped or worn down, it can make the shift drag when it passes the Neutral and heads for 2nd. You can recognize the wear as being worn on the tip of the Neutral bump, but not down at the bottom of the groove.
Also, the L" fork will show wear on the sides of the fork where it rides in the groove of its gear, if it is bent or warped. What usually warps or bends them is: the bike falls over on the left side in such a way that the shifter gets hit and lifted, but not into gear, from Neutral. Most often, I used to call this the "car-hit-it-in-the-garage" accident, knocking the bike off its sidestand, and there was something on the floor near the shifter when the bike fell over...it happened a LOT in the day.
In the end, what happens is: the shift fork cannot push the C2 gear dogs all the way into the C5 gear's slots. Sometimes, the C5 slots may also be worn, which then tapers them and makes that gear tend to push the C2 back out while you are trying to push it in. Normally, those 2 gears should be replaced as a set, or at least the 2 of them recut together to have straight dogs and slot edges.