https://academic.oup.com/hmg/article/21/26/5500/559609   5-Hydroxymethylcytosine (5-hmC) is a newly discovered modified form of cytosine that has been suspected to be an important epigenetic modification in neurodevelopment. While DNA methylation dynamics have already been implicated during neurodevelopment, little is known about hydroxymethylation in this process. Here, we report DNA hydroxymethylation dynamics during cerebellum development in the human brain. Overall, we find a positive correlation between 5-hmC levels and cerebellum development. Genome-wide profiling reveals that 5-hmC is highly enriched on specific gene regions including exons and especially the untranslated regions (UTRs), but it is depleted on introns and intergenic regions. Furthermore, we have identified fetus-specific and adult-specific differentially hydroxymethylated regions (DhMRs), most of which overlap with genes and CpG island shores.
https://www.semanticscholar.org/paper/Association-of-5-hydroxymethylation-and-of-DNA-with-Ponnaluri-Ehrlich/2121515f34ca9f0640cc7a47a07ba1f4ea050ab1
Differentially methylated or hydroxymethylated regions (DMRs) in mammalian DNA are often associated with tissue-specific gene expression but the functional relationships are still being unraveled. To elucidate these relationships, we studied 16 human genes containing myogenic DMRs by analyzing profiles of their epigenetics and transcription and quantitatively assaying 5-hydroxymethylcytosine (5hmC) and 5-methylcytosine (5mC) at specific sites in these genes in skeletal muscle (SkM), myoblasts, heart, brain, and diverse other samples. Although most human promoters have little or no methylation regardless of expression, more than half of the genes that we chose to study-owing to their myogenic DMRs-overlapped tissue-specific alternative or cryptic promoters displaying corresponding tissue-specific differences in histone modifications.
A list of all the proteins involved for the regulation of DNA methylation and demethylation is provided here: https://genomemedicine.biomedcentral.com/articles/10.1186/s13073-015-0134-6#Sec20
The function of 5-hmc and neurodegenrative disorder is mentioned in 
The emerging role of 5-hydroxymethylcytosine in neurodegenerative diseases
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4256999/pdf/fnins-08-00397.pdf