There are parenthesis, (), and there are brackets, . These are used the same way in mathematics*, but usually parenthesis are used first, and then when there are too many parenthesis groups, brackets are used to group those together - but for the most part, parenthesis and brackets are the same tool.
To answer your student's question, why can we "forget" the bracket? That is a wonderful way to put it, we can forget the parenthesis because [in the example you gave] they are meaningless mathematically. Something to bring up with your students to start things off -
Parenthesis (or brackets) are used two different ways in mathematics:
1) to visually (but arbitrarily) separate a group of symbols, so as to make them easier to see, read, and think about... kind of like saying, "hey, you really should group these together in your thinking, but you don't have to."
2) to dictate order of operation, so that there is no ambiguity as to what to do first, second, ..., last.
Your example is the number one category, so the parenthesis can be "forgotten", ignored, not used at all, it is all the same, but perhaps the mathematician wishes to emphasize the (x + 5), and so they place it in parenthesis to express that group. But without the parenthesis, the expression is the same.
Regarding example two - consider the following expressions:
a) 2 + 4 * 6 = 48
b) 2 + (4 * 6) = 48
c) (2 + 4) * 6 = 36
For example a, without parenthesis it isn't so clear what to do first, but the order of operations dictates that multiplication occurs first, and then addition, and so the expression is equal to 48. But this is easier to see with example b, and so example b is the typical way to write the expression, even though we can "forget" the parenthesis if we wanted to. However, make sure your student understands that forgetting the parenthesis in example c isn't okay, because with the parenthesis the expression is equal to 36, but without the parenthesis, the expression is equal to 48. This is because the order of operations requires that parenthesis occur before anything else. And so in this way, we can forget the parenthesis for expressions like a and b, where the parenthesis are meaningless in that the expression is computed in the same order of operation as it would have been without parenthesis, but we can not forget the parenthesis when they are dictating the order of operation to use, so that otherwise the parenthesis-less expression would equal something else.
And yes - it is amazing what those kids can get you to think about.
- This isn't true for advanced mathematics.