Going to do this one in reverse from how we normally do it, because, frankly, there wasn't that much going on five years ago, and a whole lot to say about fifteen years ago.
Citizendium, Larry Sanger's first attempt at a Wikipedia rival (he would go on to make many more), was doing fairly well at the time, but mismanagement would eventually kill its momentum. Meanwhile, in the wake of various incidents that caused chaos, it was made impossible to delete the Main Page of Wikipedia. Don't test this out. Seriously, don't. Though you might get a special barnstar if you do:
|The Destroyer of the Wiki Barnstar|
|OH MY GOD WHAT DID YOU DO THERE'S MONKEYS AND FISH EVERYWHERE SOMEONE HELP|
Finally, on a more serious note, this was also the point where controversy over Wikipedia hosting images of Muhammad reignited. There had been some controversy in 2006 when the Jyllands-Posten Muhammad cartoons controversy hit the main page, but this was the start of demands that all such cartoons be removed. In this issue's Cobwebs, we finally publish an article from 2010 about the point where we lost the moral high ground on such issues.
Lovers of regular Signpost segment the Traffic Report will find its presumptive origins in a Special Report in the 4 February 2013 issue that analysed some of the interesting trends and spikes. The film Star Trek[:] [I/i]nto Darkness caused pretty much the expected amount of controversy as to how it should be capitalised. A list of Wikipedia hoaxes provides all the fun reading one would expect.
Looking in more detail, portals were still a big deal back then; they're fairly moribund now: Featured portals would close in 2017, and there was an attempted purge in in roughly 2019. Why? It's hard to say. Perhaps as Wikipedia's search tools improved, portals ceased to be a key way to find articles; perhaps it has to do with the general decline of WikiProjects. Portal:Opera is still doing great as a way to show off content in WikiProject Opera, but there's certainly a lot fewer WikiProjects than we once had. I still remember when, if you wanted help on basically any subject, you'd just find the relevant WikiProject and ask them.