Sun, not really. For me that would be Libra and Sagittarius. I've only very briefly dated people with Sun in those signs. Although there is a Libra who's appeared in my life recently and who knows? But I have Moon and two other planets in Libra, and I have a ton of close contacts between my planets and hers. 

So I wouldn't focus on the Sun signs being 5 apart, but on the whole chart. It could be somewhat significant if the two Suns are closely inconjunct by degree. Or if other planets are. Or if one person's planet combines with the other person's chart to form a yod or something. But generally, in a long-term relationship, there are closer contacts than that. 

I remember once meeting someone and feeling super-excited. We went out a few times and it totally fizzled. Looked at the chart later and there was nothing of note connecting us. That's how it goes sometimes.

I have a different view from the populous about this aspect. I believe that this aspect is greatly misunderstood because it’s variable in nature i.e. sometimes it behaves like a conjunction and other times much like a square. This is quite evident in the aspect’s names.

According to Oxford dictionary:

Inconjunct is derived from the Latin words in meaning enter and conjunctus which means joined together, which reads “enter joined together” …. by definition sounds very much like our good old conjunction.

Quincunx originates from an early Roman coin that denoted an arrangement of five dots with four at the corners creating a square with the fifth dot at its center. …… there’s the square nature.

An aspect that is so variable in its nature it required two names that mean conjunction or square, respectively. There’s nothing minor about this aspect, it’s just simply misunderstood.

Coming to astrology, when this aspect is present, there’s often some misunderstanding between the two planets inconjunct/quincunx, but underneath that you’ll often find energy that vacillates from a conjunction to a square, and vice versa.

I don't think it's an unimportant aspect (I have two of them, near exact, forming a yod) but I understood the original post to be about just the signs being five apart, rather than an inconjunct between the Suns within a reasonable orb. And of course there's much more to synastry than an angle between the two Suns.

In many cases cases (e.g. Cancer/Sag, Aries/Virgo) you can see the tension between the signs. In my case, the quincunxes involve Taurus, Libra, Pisces. Maybe because Taurus and Libra are both Venus-ruled, and Venus is exalted in Pisces, or maybe just because I have those three signs prominent and "get" all of them, but I don't see Libra being in tension with Taurus or Pisces as much as, say, Gemini is in tension with Scorpio.

Thanks so much for the background of the words.  Also, for beginners, the orb for this aspect should be tight, I use 1 degree.

No personal long term experience with inconjuncts in synastry, but I’ve observed that sometimes it isn’t the inherent nature of an aspect or placement that determines how well two people click but rather a person’s natal familiarity with it. That thing about finding ourselves in the other, and all. 

YouTubers Jenna Marbles and Julien Solomita are a Virgo/Aries couple who’ve been together for seven years. The interesting thing is that they both have inconjuncts natally between their luminaries—JM as a Virgo Sun, Aquarius Moon, JS as an Aries Sun, Scorpio Moon. They’re really cute, and have lots of bits about their Virgo/Aries experience. They even did a podcast about their natal charts and synastry which was cool. 

Also interesting, JM’s former long term SO was an Aquarius. Seems like some people really dig it!