My opinion about the fifth coordinate in the physical sense is as follow.
$G_{AB}$: The metric for $5$ Riemannian manifold, presented in Kalzua - Klein theory, $A,B=1,\cdots, 5$.
$g_{\mu\nu}$: The metric over a $4$ Riemannian submanifold of the $5$ manifold, $\mu,\nu=1,\cdots, 4$.
The Kaluza Klein suggests that the component $G_{5A}$ is corresponded by the electromagnetic scalar $\phi$ and vector $A_{\mu}$ potentials defined over the $4$ submanifold, i.e $G_{5\mu}=\phi^{2}A_{\mu}$, $G_{55}\phi^{2}$. What was the purpose of the Kaluza - Klein theory? To unify the Einstein' s gravitation and Maxwell' s electromagnetism. Could it have been done? NO.
On the other hand, the forth coordinate of a "space-time" manifold, i.e $x^{4}=ct$, where $c$ is the light velocity and $t$ time. This doesn't mean that the forth coordinate is the time looking to the time and light, that is the fourth coordinate $\neq$ physical object. Why isn't it? The origin of the space - time concept isn't Einstein' n special theory of relativity, on the contrary it is the "hyperbolic" geometry of Minkowski. This geometry present a "null" $4$ - sphere, that is the radius zero, for the light propagation via a point source. Since such a propagation is spherical over $3$ - dimension (embedded in a $4$ - manifold), the radius of a $4$ - sphere in which a light propagates is
$$R^{2}=x^{2}+y^{2}+z^{2}-(ct)^{2}=0=null,$$
so over $3$ - sphere with radius $x^{2}+y^{2}+z^{2}=r^{2}$ the light propagation become
$$r^{2}=(ct)^{2}.$$
As seen that the fourth coordinate isn't indeed the time. Since the velocity of the light is a universal constant, it has been used as a "scalization factor" the time within the diameter. Moreover, let one take the energy (or temperature, electrical charge, mass, etc.) as a the fifth coordinates of a $5$ - manifold. What will the scalization factor (must be an universal constant) to converse the energy to diameter be? $[c]=m/s$ $[t]=s$, so $[x^{4}]=[ct]=m$. However, $[E]=J$, $[??]=m/J$, $[x^{5}]=[E\times ??]=m$. Is the $m/J$ the unit of what physical concept?
To load a physical meaning to the coordinates of the manifolds having dimensions rather than four isn't a consistent procedure. However, a connection, its curvature and the local sections on a fiber bundle have physical concepts., i.e gauge potential and strength, matter field, respectively. In my opinion, the coordinates have not any physical meaning.
Despite all them, if one will do a physical meaning loading to the fifth dimension of a $5$ - manifold, one must handle a fiber bundle which has locally the trivialization $M\times\mathbb{R}$, where $M=\mathbb{R}^{1,3}$ (Lorentzian or spacetime manifold). Therefore, one has a $5$ - dimensional "total" manifold, that is a fiber bundle whose the base manifold $M=\mathbb{R}^{1,3}$ and typical fiber space $\mathbb{R}$. On the other word a real bundle can be considered on a base 4 dimensional manifold.
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