Why is this 5 negative? I'm struggling with the difference between a negative number and a positive number that is being subtracted.

For example, when working on this inequality:
$$
2 - 5x \leq 7
$$

After subtracting 2 from each side, it is:
$$
-5x \leq 5
$$

Why is the 5 negative? Wasn't it a positive 5 in the original problem?

If it was negative, shouldn't the original inequality read:
$$
2 - (-5)x \leq 7
$$

Can someone explain this?
$$2-5\times x\leq7,$$
$$\Leftrightarrow$$
$$2+(-1)\times5\times x\leq7,$$
$$\Leftrightarrow$$
$$2+(-1)\times5\times x-2\leq7-2,$$
$$\Leftrightarrow$$
$$(-1)\times5\times x\leq5,$$
$$\Leftrightarrow$$
$$(-1)\times x\leq1,$$
$$\Leftrightarrow$$
$$(-1)\times (-1) \times x\geq(-1)\times 1,$$
$$\Leftrightarrow$$
$$x\geq-1,$$

So the $5$ is not negative. It is just multiplied by $(-1)$.
$2 + (-5x) \leq 7$

Take two from both sides

$(-5x) \leq 5$

You are adding a negative number, which is the same as taking a positive number. This can be thought of as the operator being held by the number on the right. Just as the two is positive, the 5 is negative.

eg:

$0 + (+2) + (-5x)$