Non primitive lfsr sequence
A binary sequence of period $105$ will have characteristic polynomial 
that is a divisor of $x^{105}-1$. Since $x^{105}-1$ has irreducible
factors of degrees $12, 4, 3$, and $1$, it is possible to have an LFSR
of length $4+3=7$ generate a sequence of period $105$, and that is
exactly what has happened here. Note that
$$x^7+x^6+x^5+x+1 = (x^3+x+1)(x^4+x^3+1)$$
where $x^3+x+1$ and $x^4+x^3+1$ are irreducible (in fact, primitive) polynomials of degrees
$3$ and $4$. Individually, the shorter LFSRs generate sequences of
periods $7$ and $15$: the "product" sequence has period 
$\operatorname{lcm}(7,15)=105$.