Is this a valid solution for this knight & knave problem?

Question on Quiz: Alice came across 5 island-dwellers, all of whom knew one another, that would only answer yes-or-no questions of the form "Is X a knight?" What is the minimum number of questions Alice need to ask, if in any scenario she would be able to determine the number of knights?

My Solution: Alice can ask each island-dweller the question: "Is a knave a knight?", so that X="a knave"(Since the question does not specify X to be chosen from any limited set). Each Knave would be forced to say "yes", and each Knight would be forced to say "no", revealing the answer. (There might even be a better strategy of figuring out the number of Knights with fewer questions than 5, though I haven't figured it out yet. Perhaps it can even be proven that the minimum number of questions required is 5 or otherwise)

#Logic

Easy Math Editor

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Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$