You make it seem equally likely or equally rational to believe that the Earth is 5774 years old as 15,340,50,774 years old. If this is what you're saying, then you are flat out wrong.
Scientists who have found out that our Universe is approximately 13.8 billion years old haven't just come up with that number from a dream or revelation, and they don't expect us to believe them on faith or authority. There is real evidence for the age of the Universe, and it is beyond any doubt that the estimate of a 6,000 year-old Earth is off by a horrible number of magnitudes.
Unless God The Clever One decided to create the Universe in such a way as to discredit the belief that he created it, and to hide his work, and to make everything in the Universe seem like it came about by natural means. Including creating evidence of ice-ages, ancient impacts, craters on the Moon, stars within hydrogen clouds that could have formed them, fossils in layers of Earth, streams of light forming faux images of Galaxies too far away to see in a young Universe, fake correspondence between DNA relationship and fossils and plate tectonics and geology etc. etc. etc.
Such a God would have a nice sense of humor, but you'd still have to be quite dumb to believe in him. And why would God want only the stupid ones to believe in him? Those who shrug at evidence and who believe what they believe regardless of whether the actual world conforms with their belief? If Heaven is going to be filled with such people, I'll take my chances in Hell.