Do really some Christians believe that the earth is 5000 years old?

Yes they do, it's mostly a American protestant thing. It's a extremely small but vocal minority of Christians or even Protestants worldwide.

Church Father Origen was already advocating a non-literal reading of Genesis from 220AD.

'For who that has understanding will suppose that the first, and second, and third day, and the evening and the morning, existed without a sun, and moon, and stars? And that the first day was, as it were, also without a sky? And who is so foolish as to suppose that God, after the manner of a husbandman, planted a paradise in Eden, towards the east, and placed in it a tree of life, visible and palpable, so that one tasting of the fruit by the bodily teeth obtained life? And again, that one was a partaker of good and evil by masticating what was taken from the tree? And if God is said to walk in the paradise in the evening, and Adam to hide himself under a tree, I do not suppose that anyone doubts that these things figuratively indicate certain mysteries, the history having taken place in appearance, and not literally.[15]'

St Augustine also argued that biblical text should be taken literally if it contradicts with Science and reason. So he saw the 6 day creation as not a literal representation of creation.

/r/religion Thread