"In the early 80s, to these four "classic" bases of DNA was added a fifth: the methyl-cytosine (mC) derived from cytosine." How come any biology course or book I've ever seen, whether high-school or top-university level, only teaches about four bases?
When DNA is replicated, methyl-cytosine pairs with guanine just like cytosine does. The only way to maintain the 'methylation marks' is to add a methyl group back on to the newly synthesized cytosine. When DNA is converted into RNA, which is then converted into protein, whether a cytosine has a methyl group attached makes no difference to the final protein.
So whether a cytosine is methylated or not doesn't change the DNA sequence you inherit from your parents. It doesn't change the structure of the protein produced from that gene. What it can do, is change when and where that gene is expressed - which can make a huge difference to the behaviour of the cell.
For instance, a gene such as BRCA1 could be 'turned off' because too many cytosines are methylated, and this could cause a cell to become cancerous. Or a lack of methylation could cause too much c-Myc to be produced, which could result in the same outcome. But then, there many other genetic regulatory mechanisms that can do that as well - such as histone modifications, chromatin structure, transcription factors, and probably methyl-adenine too! All these mechanisms interact to ensure genes are turned on and off at the right time and place, and this field is known as 'epigenetics'.
Methyl-cytosine is a modified version of cytosine that is a very important part of epigenetics, but since it is almost irrelevant to other aspects of genetics, I would argue that you could not consider it a 'fifth base'. Having read the paper, methyl-adenine is the same - interesting new aspect of epigenetics and gene regulation, but not a new base. Also, this paper doesn't exactly 'discover' it, we found methyl-adenine in bacteria in the 60s....
If you want to read about truly new bases, scientists actually synthesised an entirely new pair of bases last year, that can replicate and encode RNA and proteins! A seriously cool step forward in synthetic life http://www.nature.com/news/first-life-with-alien-dna-1.15179