How did the astronomers prove its so far away?
The suspected remoteness of the lensed object was confirmed when the team of astronomers made spectroscopic observations with one of the twin Keck telescopes on Mauna Kea, Hawaii, to measure its redshift (4.92), which is a measure of the expansion of space (due to the Big Bang); the larger the redshift, the greater space has expanded between us and the object. This can be used to estimate its distance.