What's the origin/reason behind the 5th and 6th Sunday post Epiphany being on the end of the liturgical year? I know that when the liturgical year has 24 or more Sundays post Pentecost, the 5th/6th Sundays post Epiphany happen between the 23rd and 24th Sunday.

FlosCarmeli13 explains it well, but to further elaborate ...  There are 52 Sunday's in every year, whether one distributes those as a calendar year (beginning the first Sunday in January) or a liturgical year (beginning the first Sunday of Advent).  Each of these Sundays will have proper Collects and readings from the Holy Scriptures.  When Easter is later in the year these will fill up the Sundays after Epiphany before Septuagesima Sunday (followed by Sexagesima and Quinquagesima Sundays, then the First Sunday of Lent).  However, when Easter is early in a year not all of the Sunday's After Epiphany Masses will be said before Septuagesima.   There will then be more than 24 Sunday's after Pentecost (the proper's of this 24th after Pentecost Mass always constitute the Last Sunday After Pentecost, the Sunday before the First Sunday of Advent), and the remaining propers of the Sundays After Epiphany (those not said before Septuagesima) are said after Pentecost, though the Introit ad other chanted portions of the Mass are repeated from the 23rd. Sunday after Pentecost.

As a result, the 52 Sunday Epistles and Gospels (I believe as appointed to be read by Pope St. Gregory the Great, but in any case as mandated by the Missal of Pope St. Pius V) are always read every year, regardless of how the date of Easter falls.