#### Answer

The solution is:
$$x = -7$$
To check if this solution is correct, we plug $-7$ into the original equation to see if both sides equal one another:
$$\frac{(-7 - 3)}{5} − 1 = \frac{-7 - 5}{4}$$
We multiply by the least common denominator of all the fractions, which is $20$:
$$20(\frac{(-7 - 3)}{5}) − 20(1) = 20(\frac{-7 - 5}{4})$$
$$20(\frac{-10}{5}) - 20 = 20(\frac{-12}{4})$$
Simplifying, we get:
$$20(-2) - 20 = 20(-3)$$
$$-40 - 20 = -60$$
$$-60 = -60$$
We see that both sides are equal, so we know that the solution is correct.

#### Work Step by Step

To solve this equation, we want to transform it so that we don't have to work with fractions. We find the least common denominator for all fractions, which, in this case, is $20$. We now multiply both sides by $20$ to get:
$$20(\frac{x - 3}{5}) - 20(1) = 20(\frac{x-5}{4})$$
Divide out the common factors to get rid of the fractions:
$$4(x - 3) − 20 = 5(x - 5)$$
We use distributive property:
$$4x - 12 − 20 = 5x - 25$$
Subtract $4x$ from each side to isolate the variable on one side:
$$-32 = x - 25$$
Add $25$ to both sides to separate the variable and the constant terms:
$$x = -7$$
To check if this solution is correct, we plug $-7$ into the original equation to see if both sides equal one another:
$$\frac{(-7 - 3)}{5} − 1 = \frac{-7 - 5}{4}$$
We multiply by the least common denominator of all the fractions, which is $20$:
$$20(\frac{(-7 - 3)}{5}) − 20(1) = 20(\frac{-7 - 5}{4})$$
$$20(\frac{-10}{5}) - 20 = 20(\frac{-12}{4})$$
Simplifying, we get:
$$20(-2) - 20 = 20(-3)$$
$$-40 - 20 = -60$$
$$-60 = -60$$
We see that both sides are equal, so we know that the solution is correct.