Modulo question with negative $60-88  \equiv \,\,? \pmod 5$
$60-88 = -28$
Then what do I do?
Please tell me how to answer this question. Thanks.
 A: When you have a negative number, like $-28 \pmod 5$, all you really need to do keep adding the modulus, or an integer multiple of the modulus $m$, to the negative number until it is zero or in $\mathbb Z_m = \{0, 1, \cdots, m-1\}.\;$
In this case, we can add any multiple of the modulus $5$ to $-28$ until we obtain zero or a positive number, if you are looking to represent the equivalence class of $-28$ modulo $5$ with the least positive integer $x$, $\;x \in \{0, 1, 2, 3, 4\}$.
So given $$60 - 88 = -28 \equiv x\pmod 5\tag{1}$$ and wanting to find such a representative $x$, we know that $5k \equiv 0 \pmod 5$, and simply choose $k = 6$ as our multiple of $5$ so we have $$5 \cdot 6 = 30 \equiv 0 \pmod 5\tag{2}$$
Adding $(1), (2)$:
$$30 - 28 = 2 \equiv x \pmod 5$$
That is, $60 - 88 = - 28 \equiv 2 \pmod 5$. 
What this all means is that any multiple $n$ of 5, added to $2$ is congruent modulo $5$ to $2$, including $-28$: The solutionS to all $$x \equiv 2 \pmod 5 = \{x\mid x = 2 \pm 5n, n \in \mathbb Z\}$$
A: As Key Ideas pointed in the comments...
$60-88  \equiv \,\,x \pmod 5$
$-28 \equiv \,\,x \pmod 5$
$-28+30 \equiv \,\,x+30 \pmod 5$
$2 \equiv \,\,x \pmod 5$
$x=5n-2$ with $n\in\mathbb{Z}$
