H-Trans

My H won't stay in 5th gears without holding it .Is it just a syncro or worse ? How much work to Find out ?

You do not have a synchronized transmission. 5th "gear" is worn, or the shift forks are worn, likely both.

Does that mean spitting tractor ?

4th fifth slider and the input shaft can be changed with just the top cover, and belly pump removal.
The clutch shaft is removed allowing the front of the trans to be taken apart to remove the offending shaft. Start looking for good used gears or New Old Stock now so you have them when you get that far. There are many posts with pictures on how to do it in the search for box under changing 4th 5th gear on an H. JimN

Most likely, the 4th/5th slider gear is worn out. It will be the internal teeth on the slider gear that are mostly gone. This is caused by doing rolling shifts from 4th to 5th gear and grinding the gear during the shift many times over the years. You do not have to split the tractor to fix it, but the work is nearly as major as a split. The top of the transmission has to come off which means you must remove the belt pulley gear assembly and to get that off, the seat, light support tower and the gas tank have to come off. The gear has to come out through the front of the transmission where the input shaft is, so that means the belly hydraulic pump, and the main clutch drive shaft have to come out and then the front input drive assembly on the transmission. It could be just a bad shifter rail or detent spring and ball, or the pilot bearing in the top shaft, but to get to that the transmission top still must come off. You need heavy lift equipment because the transmission top is very heavy and caution with the belly pump as well due to the weight of it. This job will cost quite a bit for parts, because you need several gaskets and likely shaft seals and maybe some bearings in addition to the gear that needs replaced.

I was able to replace the 4th/5th slider without removing the belly pump. Don"t ask me how as it has been awhile.

Many of the transmissions pop out of 5th, I think it happens from worn gears.

On the Hs I have worked on because they would not stay in 5th, all were cured by replacing the front mainshaft bearing. The bearing is mounted on the front of the mainshaft and rides in the back of the input shaft. When the bearing gets worn it allows the front of the mainshaft to wobble and it will walk the 5th gear out of engagement.

The bearing can be changed from the front after removing the hydraulic pump and transmission input shaft assembly.