Since the sequence is geometric, there is some constant [tex]r[/tex] such that the sequence is recursively given by
[tex]a_n=ra_{n-1}[/tex]
By this definition, you can recursively substitute into the right hand side the definition for [tex]a_{n-1},a_{n-2},\ldots[/tex] to find an explicit formula for the [tex]n[/tex]th term.
[tex]a_n=ra_{n-1}=r^2a_{n-2}=r^3a_{n-3}=\cdots=r^{n-1}a_1=-625r^{n-1}[/tex]
You know the second term, which means you can find [tex]r[/tex]:
[tex]a_2=-625r^{2-1}\implies125=-625r\implies r=-\dfrac15[/tex]
So, the 7th term of the sequence is
[tex]a_7=-625\left(-\dfrac15\right)^{7-1}=-\dfrac1{25}[/tex]
