Relationship between type 5 and type 3

The observer and the chameleon

Sherlock Holmes (Sherlock)
Mary Crawley (Downton Abbey)

Attraction

It is a very complementary relationship because they have commonalities that are essential to them and differences that complement them.
The 3 is attracted by the creativity, depth of thinking, ingenuity, and analytical skills of the 5.
The 5 is attracted by the self-confidence, charm, sociability, and effectiveness of the 3.
The 3 completes the 5 with his social and diplomatic skills, while the 3 greatly appreciates the constructive advices that the 5 can give him to improve himself.
Both are not very sentimental, but sensitive, and communicate their emotions rather through actions.
Both tend to seek competence and excellence in everything they practice, and can help and support each other in moving toward their goals.

Points where to be careful

Both are pretty much work-oriented, without being very emotional, and may have trouble finding time for them intimate.
The 3 might sometimes see the 5 as being too analytical, detached, and having trouble getting involved in the outside world.
The 5 may have trouble with the social needs of 3, and need more time alone, which can be a source of conflict if they fail to find a balance that suits both of them.