My transmission hesitates for several seconds sometimes before going into gear, happens 5 percent of the time. have to wiggle the shifter to get it to go.

There could only be a couple possibilities for this to happen. First, with standard shift transmissions the shifter linkage could be worn being that it only happens with 3rd and 5th gears, as this shifter slide works for both of these gears. If this is the case it is only a matter of visually inspecting the linkage for worn or broken parts and replacing them or adjusting the linkage which is the inexpensive fix that I hope you are looking at. Second, This could be caused by the syncronizers within the transmission are going bad/worn or broken. In either case the transmission will need to be removed and repaired or replaced which is the expensive route that I pray is not the way you have to go! I hope that this is some help.

CHECK FLUID LEVEL

Does that transmission have external shift linkage? Sounds like a linkage broke or the neutral gate is way off.

I take it that you have a standard transmission ? there is no adjustment, but on the saturns the plastic insert on the shifter lever (remove the center console) is what breaks, Napa auto parts has the replacement part for about $20, or you can go to saturn and spend $200 on replacing both cables

The transmission many to relearn shift points which can take several miles of driving is some cases. drive the car for a while, the hesitation in shifting continues have your dealer flash the ecu

Well check if your gear shifter cable is not broken or off loose. Have somebody wiggles the shifter while you look around the transmission and see whets going in on. Good luck

So you answered your own question
Check out the neutral safety sw (wiggle shifter, starts) or trans selector sw,whichever applies

Double check all your ground cable & + connections for clean, tight & in good shape. Sometimes just loosening them & wiggling them, then re-tightening will get better connection. Try moving shifter into neutral when this happens also, as well as turning key to start as you move shifter slowly through all gears to see if it try's even for a second to turn over. If moving shifter gets any sign of a kick over, it's probably safety neutral switch.

check transmission fluid if dirty change it and check the level first

Sounds like the car is just slipping out of gear. Keep your hand on the shifter when you back up next time. See if you can feel the shifter move when the car comes out of gear. If the shifter moves up when it happens keep pressure on the shifter holding it back like you dont want it to move forward. And of course if the shifter moves back when it comes out of gear, put forward pressure on the shifter so it doesnt slip out. This might work for now but but i know i wouldnt want to spen 700 for that ****. Let me know how it goes.