Long comment
Maybe, a more lengthy approach can help, considering the case of a single atom $p$.
Let $F$ a formula and let $p$ a propositional symbol occurring in $F$. This means that the formula is a truth-function $F(p)$: for every truth value assigned to $p$, the truth table corresponding to $F$ will outputs a truth value.
But $F$ is a tautology: thus for every assignments of truth values to atoms, the truth table will produce the value TRUE.
Consider now the formula $F' := F[A/p]$, where $A$ is a formula whatever. Irrespective of the "form" of $A$, every assignment will output either TRUE or FALSE as truth value for the formula.
Thus, when $A$ is evaluated to TRUE, we have to consider the lines in the original truth table for $F$ where $p$ is evaluated to TRUE. Due to the fact that $A$ is a tautology, in those lines the formula $F$ has value TRUE; thus also $F'$ will have TRUE in those lines.
But also when in the original truth table for $F$ the atom $p$ is evaluated to FALSE, the corresponding lines for formula $F$ have value TRUE; thus also $F'$ will have TRUE in those lines.
The argument can be iterated, taking into account that a formula is an expression of finite length and thus only a finite number of atoms occurs into it.
I see where you're coming from, but that is not what the definition means by "unknown". They are thinking of a statement like "Every even integer greater than 4 can be expressed as the sum of two primes". That is definitely either true or false, but we don't know which one.
$5x+2=10$ is a statement whose truth or falsity depends on the value of the variable $x$, so this is a very different situation. I would use the word "predicate" to describe this situation, but your textbook or teacher may have a different idea of how the vocabulary shakes out.
Best Answer
The claim is not a claim of the form that is considered in propositional logic -- it belongs squarely in predicate logic.
Some authors of introductory texts go to the trouble of defining a quasi-formal concept of what the word "proposition" means. Usually not much is actually done with this concept and it is forgotten about completely when you get to define propositional logic formally. Often it looks like the main purpose of offering the definition is to attempt to explain why it's called "propositional" logic.
Unless you anticipate being asked "is such-and-such English sentence a proposition?" in an exam, I would not worry about a particular author's definition of the word. It is not going to be important.