It is perhaps useful to first pause briefly to review what a redshift of z = 5 actually means, and why it matters.
Redshift, z, is, of course, simply a straightforward way to quantify the ratio of the observed wavelength (λo) to the emitted wavelength (λe) of light:
The longitudinal relativistic Doppler effect is:
and so z = 5 corresponds to a recession velocity of v = 0.946 c (where c is the speed of light in vacuum).
However, in a Universe with matter, at least some of any observed redshift should be attributed to gravitational effects, and in any case the precise recessional velocity of a galaxy several billion years ago is of little real interest. What is more helpful is to recognise that the stretching of the wavelength of light simply reflects the overall expansion of the Universe, i.e.
where R(t) is simply the scale factor which describes the time evolution of our apparently isotropic, homogeneous Universe.
Thus, when we observe a galaxy at z=5 we are observing light which was emitted from that galaxy when the Universe was 1/6th of its present size (and at the highest redshifts currently probed, z ≃ 9, the Universe was 1/10th of its present size).
The precise age at which the Universe was 1/6th of its present size of course depends on the dynamics of the expansion. With our current "best-bet" concordance cosmology of a flat Universe with a matter density parameter of Ωm = 0.27, a vacuum energy (or dark energy) density parameter of ΩΛ = 0.73, and a Hubble Constant H0 = 71 km s-1 Mpc-1 (WMAP7; Komatsu et al. 2011; Larson et al. 2011), z = 5 corresponds to an age of 1.2 Gyr, equivalent to ≃ 9% of current cosmic time. Thus, to a very reasonable approximation, the study of the universe at z > 5 can be thought of as a direct window into the first Gyr, or first ≃ 10% of the growth and evolution of cosmic structure.
Finally, at the risk of stating the obvious, it must always be remembered that different redshifts correspond not only to different times, but also to different places. Thus, when we presume to connect observations of galaxies at different redshifts to derive an overall picture of cosmic evolution, we are implicitly assuming homogeneity; i.e. that "back-then, over there" is basically the same as "back-then, over here". For this to be true it is crucial that surveys for high-redshift galaxies contain sufficient cosmological volume to be "representative" of the Universe at the epoch in question. As we shall see, at z > 5 this remains a key challenge with current observational facilities.