Euler The least number n that φ(n) $\small\ge$ 5? 

What is the definition of the totient function? What numbers did you explore? Did you see any patterns? 
The number is n $\small\ge$ 13, but I don't know how to prove it. The φ(n) = the number of numbers from 1 to n that are relatively prime to n. 
7? 
No; if the question were the least number N prime that φ(n)$\,\small\ge\,$5 for every n prime $\ge$ N then you'd be right. 
I don't see why you want to put so many conditions in there. But whatever. 
The intended problem seems to be to find the least number N such that φ(n)$\,\small\ge\,$5 for every n $\ge$ N. 
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It's probably easier to use a number considerably greater than 13, then verify the result for lower numbers by reference to a list of values of φ(n). 
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