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It is a linear expression.
y - x5 is an expression, not an equation. Furthermore, it is polynomial of order 5 and a non-linear function cannot be expressed in slope-intercept form.
A polynomial is a linear combination of non-negative integer powers of a variable. A linear combination means you can multiply the terms by constant numbers before summing them. The terms can consists of only positive integer powers of the variable or a constant.
It could be a function or a linear expression.
That is not a valid equation because the linear expression is not a polynomial. You can't have a variable in the denominator.