In the laws of thermodynamics, the fifth law of thermodynamics is any of a number of various, yet unsubstantiated, postulates, theories or (sometimes) humorous statements positioned to explain facets of physical phenomenon or existence; often stated on the assumption that the vacancy of the fourth law of already clearly filled by those such as the Onsager reciprocal relations (1931) or Odum’s maximum power principle (1955), etc. [1] A 1961 reference gives the following example of a common fifth law: [2]

“That no experiment gives quite the expected numerical result is sometimes called the fifth law of thermodynamics.”

In 2004, to cite another interpretation of a fifth law of thermodynamics, authors David Bailin and Alexander Love stated: “The man who discovers a fifth law of thermodynamics will have a great difficulty in finding a suitable name.” [3]

Discussion
It is sometimes argued that American physical chemist Alfred Lotka was the first to postulate the need for additional laws of thermodynamics, when in 1922 he stated: [4]

“The principle of natural selection reveals itself as capable of yielding information which the first and second laws of thermodynamics are not competent to furnish. The two fundamental laws of thermodynamics are, of course, insufficient to determine the course of events in a physical system. They tell us that certain things cannot happen, but they do not tell us what does happen.”

In this statement, to note, we see that Lotka is off-logic in his view. If, for instance, he would have read the works of those such as Hermann Helmholtz (1882) or Walther Nernst (1893) he would have learned that the measure of affinity A in a physial system, being a function of the first and second law via the equation:

where, T is the temperature of the system, ΔS is the change in entropy for the process, and ΔH is the change in enthalpy for the process, does tells what happens in a physical system, in that movements, evolutions, reactions, etc., will proceed in the direction of the affinity satiety or, in modern terms, in a direction such that individual chemical species are said to move along paths of minimal free energy. [5]

References
1. Jorgensen, Sven E. and Kay, James. (2001). Thermodynamics and Ecological Modelling (pg. 70). CRC Press.
2. Anon. (1961). ISIS (pg. 165), Vol. 52.
3. Bailin, David and Love, Alexander. (2004). Cosmology in Gauge Field Theory and String Theory (pg. 24). CRC Press.
4. (a) Lotka, A.J. (1922a) 'Contribution to the energetics of evolution'. Proc Natl Acad Sci, 8: pp. 147–51.
(b) Lotka, A.J. (1922b) 'Natural selection as a physical principle'. Proc Natl Acad Sci, 8, pp 151–4.
5. Nernst, Walther. (1895). Theoretical Chemistry: from the Standpoint of Avogadro’s Rule & Thermodynamics (section: The Measure of Affinity, pgs. 586-88). MacMillan and Co.