Take it to get the gearbox replaced.
There are several things that can cause your 2005 Jeep manual transmission to shift hard between first and second gear. The most common cause is a malfunctioning shifting fork.
The biggest problems of why a jeep wont go into third gear is either that the shifting fork for third gear is worn or bent or the sycronizer or gear itself is worn out and needs to be replaced. Once you take the top of the transmission off where the shifter is located you can see the whole transmission gears and inspect the shifting forks. A general rule of thumb is to make sure the transmission is in second gear before taking the top off. This will make it easy to take off and rerattach the top of the transmission cover and align the shifting forks.
A 2000 Jeep automatic that is not shifting correctly after it gets hot might have something wrong with the speed sensor that is located in the transmission. The speed sensor tells the transmission what gear to shift into at certain speeds.
The first cause of the jump out from one to other gear is the loose shifter fork, which connects the shifting linkage and gears of the transmission. The second cause is loose shifting linkage itself, which connects the gear shifting knob and shifting fork. The shifting linkage and shifting fork become loose due to the rapid changing of gears from one gear to other at high speed of vehicle. The third cause is the misalignment of shifting linkage to the shifting fork.
Your synchro is most likely going bad, the same one works for 1st and 2nd so 2nd should be giving you trouble too.
Down from neutral for first gear and up for the rest
maybe you broke something!
check the exhaust system
There are several things that can cause your manual transmission not to shift out of first gear or reverse. The most common cause is a broken shifting fork.
First, check transmission fluid levels, but typically once you loose a full gear, if the fluids topped off, your looking at a transmission rebuild.
Your synchro's are going bad, common problem with the ax5. The synchro gear will match the speed of the two gears so they meet smoothly, when these wear out you will get difficult shifting and some grinding.
if it is an auto, you will have slippage even though the fluid has been replaced and filter changed, it will have a hard time shifting and may even be stuck in one gear. For a manual, you will have a very difficult time shifting ( clutch is ok ) downshifting will be almost impossible and you may get permanently stuck in one gear.