1. Leptotene (D) : This is the first stage of Prophase I. During this stage, the chromosomes begin to condense and become visible under a microscope.
2. Zygotene (A) : In this stage, homologous chromosomes begin to pair up, a process known as synapsis. This pairing forms structures known as bivalents or tetrads, which allow for crossing-over (exchange of genetic material) to occur.
3. Pachytene (B) : This is the stage when crossing-over occurs. Recombination nodules appear where the crossing-over has occurred. These are the physical manifestation of genetic recombination, which increases genetic diversity.
4. Diplotene (E) : At this point, the homologous chromosomes begin to separate, but remain attached at points called chiasmata. This separation of chromosomes is called desynapsis.
5. Diakinesis (C) : This is the final stage of Prophase I. The chiasmata move to the ends of the chromosomes, and the nuclear membrane breaks down, signaling the end of Prophase I.

So, the correct order of the stages is: Leptotene, Zygotene, Pachytene, Diplotene, and Diakinesis. Hence, the correct answer is Option C: (D), (A), (B), (E), (C).