The first way is the argument from motion [which requires a first Mover] … The second is from the nature of efficient cause [the chain of causation requires an uncaused Cause] … The third way is taken from possibility and necessity [roughly, ‘why there is something rather than nothing’ requires a necessary being] … The fourth way is taken from the gradation to be found in things [comparisons, e.g. ‘hotter’, relate to a perfect standard, ‘hottest’, so overall to God as the cause of perfection] … The fifth way is taken from the governance of the world [that things are evidently designed to an end, requiring a Designer]. (ST I, qu. 2, art. 3).
The first four are related to the Cosmological Argument, the fourth remotely to the Ontological Argument, the fifth to the Teleological Argument.
"Quinque Viae." The Concise Oxford Dictionary of World Religions. . Encyclopedia.com. (September 10, 2018). http://www.encyclopedia.com/religion/dictionaries-thesauruses-pictures-and-press-releases/quinque-viae
"Quinque Viae." The Concise Oxford Dictionary of World Religions. . Retrieved September 10, 2018 from Encyclopedia.com: http://www.encyclopedia.com/religion/dictionaries-thesauruses-pictures-and-press-releases/quinque-viae