...and is not null

I think what you are looking for is a compound condition:

     SELECT * FROM my_table WHERE my_column != 5 OR my_column IS NULL;

This is because what you are selecting for is two conditions: when the value is != 5 and when the value is NULL so the result of != 5 is unknown.

FWIW I agree with you that NULL's are counter-intuitive. While I am more or less aware of all the various ways to account for them, I still gravitate towards SQL schemas without NULL's since I prefer the intuitiveness of 2VL when writing or reading SQL.

Something along the lines of

  COALESCE(my_column, -1)

might work for you in this case. See [1] for documentation on it in Postgres (it is in ANSI SQL though).

[1]: https://www.postgresql.org/docs/current/functions-conditiona...