What is the meaning of $\mathbb{Z}_{5}^{+}$ (and $\mathbb{Z}_{5}^{*}$) in group theory? What does $\mathbb{Z}_{5}^{+}$ mean? I know $\mathbb{Z}_{5}$ represents the set of integers modulo 5. I would assume this would mean it is the set of integers modulo 5 under addition except that normally this is notated as $(\mathbb{Z}_{5},+)$. I'm confused as to the meaning of this notation? 
Edit:
Furthermore, what is the meaning of $\mathbb{Z}_{5}^{*}$. The context I saw this in seems to imply this is a group but if it was the same thing as $(\mathbb{Z}_{5},*)$ it couldn't be since $(\mathbb{Z}_{5},*)$ lacks some inverses.

For $p$ prime, $\mathbb Z_p^*$ is used to denote the multiplicative group of nonzero elements of $\mathbb Z_p$.
On the other hand, $\mathbb Z_n^×$ denotes the group of units modulo $n$, which has order $\varphi (n) $, where $\varphi$ is Euler's totient function. 
For prime $p$, we have $\varphi (p)=p-1$, and indeed $\mathbb Z_p^*=\mathbb Z_p^×$.
