(5) A Hint: From the definitions of monotonicity and oddness, we know that the function is a monotonically increasing odd function.
(5) The function $f(x)=\left\{\begin{array}{ll}1-5^{-x}, & x \geqslant 0, \\ 5^{x}-1, & x<0,\end{array}\right.$ is ( ).
(A) Monotonically increasing function, odd function
(B) Monotonically decreasing function, even function
(C) Monotonically increasing function, even function
(D) Monotonically decreasing function, odd function