Reading through your postings I'm going to suggest a complete do-over -- re-flash your On5 with its stock ROM so you get your phone back in working condition, and then if you want to root it again go on from there. Keep in mind with a dated phone that only has 1.5GBs of RAM it simply will have some performance issues no matter what you do, rooted or not.
http://www.gsmarena.com/samsung_galaxy_on5-7648.php
Not knowing were or which ROM you used, try re-downloading one from here, either sammobile or updato. Both are good sources for stock Samsung ROMs. Be absolutely sure you're selecting the ROM for your model, there's no fudging involved with these older ROMs, no mix-and-match, no substituting one that's 'close enough'. I have suspicions that's what happened initially, the ROM was a mis-match. ROMs are very model specific. Anyway, do a search for your model of Galaxy On5:
https://www.sammobile.com/firmwares/
or
http://updato.com/firmware-archive-select-model
With sammobile, at the bottom of the actual download page there are instructions on how to flash the ROM. Side note: it refers to the latest version of Odin but in your situation that might not be advisable. Odin is not very backwards compatible so using an older version that matches what you're working on should work out better:
http://www.droidviews.com/download-odin-tool-for-samsung-galaxy-devices-all-versions/
Also note that sammobile intentionally restricts the download speed of its download servers so do not be surprised if the download takes quite a long time even if you have a fast connection on your end (ROMs are usually sizable, 1GB+). If you opt to use updato the same process to flash the ROM still applies.
Once you flash the stock ROM and get your phone working again, it will be unrooted again. Just to clear up some misconceptions you have, in order to unroot your On5 you have to flash the ROM. A Factory Reset won't have any affect at all as far as rooting or unrooting your phone. When you do a Factory Reset the only thing it does is wipe the general user data partition, removing any user data and the apps the user has installed. The Android operating system on your On5 is stored in separate and different partitions, that a Factory Reset has nothing to do with. Doing a Factory Reset will leave a rooted phone as rooted, it doesn't have anything to do with the operating system itself.
Also, wiping the system cache partition has nothing to do with whether your phone is rooted or not rooted. The cache partition is dedicated solely to the operating system's own cache so it's completely separate from the typical app caches in your phone's user data partition. It's generally a good idea to wipe the system cache whenever you perform a system upgrade or do something like re-flash the ROM, the process itself only takes a few seconds. It does need to be done while your phone is running in its Recovery Mode (power off your phone, and then while simultaneously holding down the Volume Up, the Home, and the Power buttons). As you've already encountered, your phone can be booted up into three distinct states -- Recovery Mode, Download Mode (simultaneously holding down the Volume Down, the Home, and the Power buttons), and the regular start up you always use your phone in. (There's also Safe Mode but that's not relevant right now).
Anyway hopefully at this point your phone is working again. If you really feel it's necessary to root it again, where you following a procedure like this to root it before?
https://www.obeygeek.com/how-to-root-samsung-galaxy-on5-sm-g550t-and-sm-g550t1/
https://www.obeygeek.com/how-to-install-twrp-recovery-on-samsung-galaxy-on5-sm-g550t-and-sm-g550t1/
If you do try this again, read through
all the instructions to familiarize yourself with the whole process, maybe a couple of times even. Then go ahead and do each step one at time following the directions as stated, don't improvise or take any shortcuts.
