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Understanding the distributive property is crucial when you're subtracting polynomials. It refers to the way numbers are distributed across parentheses when they are being multiplied or, as in our case, when there is subtraction or addition outside the parentheses. For instance, if you have an expression like \(a(b + c)\), the distributive property allows you to expand this into \(ab+ac\).

When dealing with subtraction, as in the exercise \(5b - (3b + 5)\), we need to distribute the subtraction sign across the terms inside the parentheses. This changes the sign of each term within the parentheses, thereby turning \(3b+5\) into \( -3b - 5\). This step is pivotal as it prepares the expression for the combination of like terms and further simplification.

Once you've distributed the negative sign, the next step is combining like terms. Like terms are terms that have the same variables raised to the same power. Simply put, they 'look' similar. For example, \(2x\) and \(3x\) are like terms, whereas \(2x\) and \(2y\) are not.

In our exercise \(5b - 7 - 3b - 5\), \(5b\) and \(3b\) are like terms, as are the numbers \(7\) and \(5\) (these are constants). When you combine \(5b - 3b\), you get \(2b\), and combining \( -7 - 5\) gives you \( -12\). This step is all about recognizing patterns and simplifying the expression.

Simplifying expressions is the final and most satisfying step. It's where you bring together all your previous work to form a simpler expression or, when possible, a single number. After distributing and combining like terms, you may still have an expression that can be more compact. In this exercise, after combining like terms, we get \(2b - 12\).

There's nothing more to combine here, as \(2b\) and \(12\) are not like terms. So the expression \(2b - 12\) is already in its simplest form. The goal of simplifying is to make the expression as clear and as easy to work with as possible, whether that's for solving equations, graphing lines, or interpreting the results in the context of a real-world problem.