I have to define a state space equation. there is a vector with 5 members as stats such that all states(members of the vector) are real numbers.
which notation is true for this case?
x=[x1,x2,x3,x4,x5] ∈ R
or
x=[x1,x2,x3,x4,x5] ∈ R^5
where ^ implies that the number 5 is the power of R
is both are correct. which one can I use to introduce my states?
In general, the symbol $\mathbb R^n$ is used to denoted the vector space of $n$-dimensional real vectors. The symbol $\mathbb R$ is typically used to denote the set/field of real numbers, not a vector space.
With this in mind, both of the following notations would likely be readily understood:
$$\mathbf x =\langle x_1, x_2, x_3, x_4, x_5 \rangle, \quad \mathbf x \in \mathbb R^5$$ or $$\mathbf x =\langle x_1, x_2, x_3, x_4, x_5 \rangle, \quad x_i \in \mathbb R$$