Have you attempted the tests you listed with poor results? Or just looking for more effective, efficient, simple, or accurate tests?
Sorry if I seem confused, but "good" doesn't give me much to go on. What's good to me may not be good to you, whether something is good varies even with the individual according to task, for example: one may search for the most accurate way or the most expedient way, the two may, or may not, be the same, When one says "good" it can probably be assumed the one they are seeking to them is "good," but if what they seek is unknown to you how can you tell which is good? Without being more specific about what you're looking for, the best I can do is guess, and that's probably not much help to you.
Are the five compounds in a mixture requiring separation? I'm guessing you were given five individual samples. Yes, there are other good ways, quite a few of them, but to my knowledge all have downsides; higher cost, greater risk, more complexity, so on, and so forth. For example: chromatography, or use of an analytical reagent. So it's most sensible, often necessary, to narrow down the possibilities first with the simple tests.
It just occurred to me that I asked your same question myself back sometime in the 1950s, it was a little hard to believe those primitive tests were it, there had to be better more advanced modern jet-age ones. There were not and to my knowledge, for the most part, and although a couple tests are no longer part of the analytical process such as tasting unknown substances, there still isn't. These simple tests have been in use for quite some time and I expect they will continue to be. All are inexpensive, readily available, require little training or skill, and to a point they do work surprisingly well.