Find locus of point

If a complex number z satisfies $log _{frac{1}{2}}left(frac{|z|^{2}+2|z|+6}{2|z|^{2}-2|z|+1}right)<0$, then locus of point represented by z is

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Since $log _{frac{1}{2}}left(frac{|z|^{2}+2|z|+6}{2|z|^{2}-2|z|+1}right)<0$

$therefore frac{|z|^{2}+2|z|+6}{2|z|^{2}-2|z|+1}<1$
$Rightarrow|z|^{2}-4|z|-5>0$
$Rightarrow(|z|-5)(|z|+1)>0 Rightarrow|z|>5 text{ and } |z|<-1$

But the ans is given in the question is $|z|<5$

Am i wrong???