Most of the time remotes hydraulic outlets are used to move hydraulic rams. They could be for a top link or to lift something off the ground like a disk, planter, cultivator, pull-typ brush hog, dump trailer and of course your front end loader (same concept different location). You can also plumb into them and put lines running up to your bucket so you can use a grapple, tree shear, round bale grabber, etc. The only thing that I have that uses two hookups is my field cultivator which uses one set to lift up the wheels and one set to fold up the wings.
In some cases you can use the hydraulic to run hydralic motors like an hydraulic auger on a fertilizer/seed tender or on some planters.
In some other cases, if you have higher flow, you can use them for dirt augers, hydraulic brush hogs, hydraulic rototillers, etc. I would think that would be pushing it on the U5030 but you'd have to look at the specs closely for that. The thing they look at is flow rate, pressure and cooling capacity. When you pump a lot of oil like that it gets hot.
Most log splitters attached to a tractor, (via 3-pt), that I've seen don't use the remote hydraulics but have it's own hydraulic pump running off the PTO of the tractor. You probably wouldn't want to consider that anyway as running a 50hp tractor to run a log splitter that can be run with a 5 hp motor is not very efficient.