The general rule of thumb for root locus is that the branches can only cross the real axis to the left of an odd zero or pole
Yet, I have seen examples where the opposite is true, where it crosses on even poles and zeros
For example $Gp(s)=(1-s)/s(s+5)$
What is the rule for this?
If $kG(s)=k\frac{N(s)}{D(s)}$, the root locus of $G(s)$ shows the location of the roos of $D(s)+kN(s)$ by changing the values of k. Now, you should know that the values of k are real and can be between $(-\infty,+\infty)$, but it seems you only consider the values between $[0,+\infty)$. The rlocus function in MATLAB also considers the values between $[0,+\infty)$, and if you want to get the root locus of $G(s)$ for $k \in (-\infty,0]$, you should use the script 'rlocus(-G(s))'.
By understanding all these, I can explain what is your mistake:
If you want to use the rule of thumb for positive $k$, you should make $G(s)$ in its standard form, which is $G(+\infty)$ should be a positive number or be $0^+$ but not $0^-$. That is to say, you can use the rule of thumb for $\frac{s-1}{s(s+5)}$ but not $\frac{1-s}{s(s+5)}$. If I want to explain more, I can say that the root locus of $\frac{1-s}{s(s+5)}$ for positive k is equal to the root locus of $\frac{s-1}{s(s+5)}$ for negative k. So, you have two options to use the rule of thumb: whether consider the root locus of your function for negative k or consider the root locus of $-Gp(s)$.