Testing a CAT5e run can really only be done with a good tester. I use a certification test tool and it runs through all the parameters required of a CAT5e or whatever type of cable certification I need. Then it tells me exactly where in the cable any problems are and what they are. Neat, but expensive. The cheap continuity testers are practically useless, except for miswired cables. Probably you don't have access to the good testers, but it is what you really want.
The problems that cables have are many and varied. But from your post, if your cable is not performing up to snuff, there are a couple likely culprits, namely how 'well' the cable ends were attached by yourself and your tools and the quality of the cable itself. Making your own cables is troublesome. Female ends need to be of the correct type CAT5e, CAT6, etc. for the intended network speed, the cable has to be stripped just so, and not unwound too much and according to spec, and the crimp tool has to make a uniformly good crimp. Metal, not plastic tools are best with good metal crimp dies. Of course, the cable itself has to be 'good', and unfortunately there is 'bad' cable out there and it's impossible to tell without a tester. It all sound too simple, but these little things can cause many problems.
The best way to avoid pitfalls is to only buy name brand high quality patch cables with molded ends for the length you need. Or get someone with the right equipment to make custom cables for you. The cheap patch cables you can buy often have lots of problems, I've tested many that are total crap.
But back to your issue, network cables will work 'sort of', even if they are not up to spec. The nature of Ethernet is such that it can detect errors in transmission as a result of cabling problems ... and then just do a resend. or many resends of the same packets. So what you may see is a slow transmission, or breaks in transmissions, or nothing really noticeable at all. Which is why a good tester is essential for making cables.