It must be 7!

Level pending

$a+b+c=1 \\ a^3+b^3+c^3=3 \\ a^5+b^5+c^5=5$

Let $$a,b,c$$ be complex numbers satisfying the equations above. What is the value of $$a^7+b^7+c^7$$ round up to the closest integer?

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