If all variables are a subset of the candidate key, is the database design 5NF?
If all variables are a subset of the superkey, is the database design
  5NF?


In any 1NF table (does not have duplicate rows) the whole header is a superkey. Any set of attributes (columns) from that table is a subset of that superkey. If your reasoning were right that would mean that any 1NF table is in 5NF. So, this is not correct. But, you are probably just misusing terminology.

What you are probably asking is what if the whole header is the (candidate) key -- keep in mind that a key is irreducible.

General answer to this question is again no; just because a table is all-key it does not make it automatically in 5NF -- all key tables are in BCNF (3.5). They are likely to be in 5NF too, but not as a rule.

Given the info you have provided, I am not sure if your table is all-key (in BCNF). For example, is there a FD {Message} --> {Level} ? 

So to answer this properly, you would have to provide sample data and some spelled-out "business" rules.

Take a look at

https://stackoverflow.com/questions/18029821/how-to-understand-the-5th-normal-form