Alex's work for the following quiz problem is as follows: Is Alex correct? if it's incorrect, what is the correct solution?

Answer:
see explanation
Step-by-step explanation:
[tex]\sqrt{10}[/tex] and [tex]\sqrt{5}[/tex] cannot be simplified as they are already in simplest form.
Note that [tex]\sqrt{10}[/tex] + [tex]\sqrt{5}[/tex] ≠ [tex]\sqrt{15}[/tex]
Thus
2[tex]\sqrt{10}[/tex] + 5[tex]\sqrt{5}[/tex] ← cannot be simplified any further