While transcription of rRNAs happens in nucleolus mediated by RNA Polymerase-I, we see that 5S-rRNA is transcribed elsewhere by RNA Polymerase-III. What is the cause and why?
The three RNA polymerases (RNAPs) are very similar to each other, yet not identical. As described in this article, there are subunits that are specific for each type of polymerases.
In addition to providing unique substrates that polymerase-specific subunits bind to give each of the RNAPs their specific functionality, the two largest subunits also shape the active site cleft of the enzymes where the transcription reaction occurs.
The results of the linked article also claim that even though the cleft loops are conserved regions, there are significant length differences between the three polymerases.
Also rRNA gene is similar to the tRNA genes and they differ from other genes in the recruitment of the polymerases. "Traditional' promoters are located upstream the start site, while 5s rRNA gene and tRNA genes have one and two boxes respectively that recruits RNAPIII.
The 5s rRNA and tRNA genes have promoters within the coding region of the gene.
Here are two images form the linked page:
In this article it is described that 5s RNA genes have translocated severeal times throughout evolution, and on of the mechanisms for this could be analogous of the second class of SINE elements, that contain internal RNAP III promoters, and are derived form tRNA (this could also indicate the similar structure to tRNA genes).
From this good review Evolution of multisubunit RNA polymerases in the three domains of life I'd like to take one short quote that might help:
...The structure and function of some of these factors are conserved across the three domains, whereas some non-homologous factors show an intriguing level of structural and functional similarity, suggesting that convergent evolution has led to alternative means of facilitating the same process.
This article suggests RNA Pol III formed early in eukaryote evolution, and while there's a lot of conservation, the enzyme-specific subunits result from divergent evolution. Another article suggests the actual increase of subunits, however, is a result of the permanent recruitment of transcription factors to the core RNAP by studying homology of subunits to existing TF's. So if you were to ask why another polymerase? The article suggests gene duplication events. There are homologs for every RNAPII subunit in archaea, and and the subunits unique to RNAPI and III are homologous to transcription factors for RNAPII (TF's denoted TFII...). They further conclude that,
The first RNAP duplication event(s) likely resulted in two RNAPs: RNAPI and the ancestral RNAPII/RNAPIII. This is supported by the existence of three homologous proteins that are found in the RNAPII and RNAPIII transcriptional systems but with no homologs in RNAPI. The first two proteins are TFIIE a and b that are found in RNAPII and that are homologous to RPC82 and RPC34 in RNAPIII, respectively. In contrast, RNAPI lacks a homolog of either subunit of TFIIE, indicating a loss of TFE in this RNAP. Thus, the ancestral TFE was likely lost along the RNAPI lineage but maintained in both RNAPII and RNAPIII following duplication of the RNAPII/RNAPIII ancestor. The third such protein is the archaeal TFB, which is common to both RNAPII (where it is named TFIIB) and RNAPIII (where it is named TFIIIB-BRF) but absent from RNAPI (fig. 4). These recruitment events resulted in the expansion of the number of RNAP subunits from 12 in the ancestral eukaryotic RNAP to 14 in RNAPI (Kuhn et al. 2007) and 16 in RNAPIII (17 if we include the unikont- and plant-specific RPC31 protein; Proshkina et al. 2006).
So in speculation, if you had to ask why a different polymerase, the evolution of the two lineages of RNAP's dictated a different binding/initiation motif for what are perhaps (retro)viral or (retro)transposable elements [the tRNA and 5s rRNA genes]. This is still under investigation, however.