In DnD 3.5, the system by default only gives significant XP for killing things (monsters, vermin, shopkeepers, etc), which often leads to player characters becoming "murderhobos" in an effort to maximize rewards. I have the 5e PHB, but it doesn't say much about how you get XP other than to point out the sample monsters are worth XP when killed. Does the system address the murderhobo problem in any way? Do any of the design articles discuss this issue as they have other classic issues?
In hoard of the Dragon queen, the recently and first published adventure for the official d&D Tyranny of Dragons story line, it's says that you can either give out xp for killing monsters as well as the various xp given out for plot related tasks or you can use the optional 'milestone experience rule' which means characters go up a level after certain events (likely unrelated to killing things)
Other examples in the module say things like :
This assumes of course that you find the murderhobo style of swords and sorcery to be a problem.
To see the original revelation of this new design decision you can read the archive of the Legends and Lore: Experience and Levels article.
To answer this question, let's briefly examine murderhoboism. This is an affliction where players do nothing but wander around killing NPCs and taking their stuff. But muderhoboism is really about what players are not doing. They're not roleplaying, they're not getting involved in the plot, they're not becoming productive participants in the world the GM has established for them.
I'd argue that 5e takes a positive-feedback approach to the murderhobo problem. Rather than denying players XP for monster kills (which would be a sweeping departure from D&D tradition), it gives them incentives for roleplaying well. 5e gives all characters detailed character backgrounds that encourage you to think about your character's history in the world, complete with keepsakes from your past adventures. It encourages you to devise flaws and bonds during character creation that connect you with the world and the rest of the party. The rules for Inspiration provide DMs with an easy way to provide characters with mechanical benefits for good roleplaying.
So rather than punishing players for playing D&D "the wrong way", the new edition gently guides them into the Path of Roleplaying by encouraging good behavior. I think that's a good approach to take; murderhobos wouldn't adopt a system which did otherwise.
Aside from the fallacy in the question, which I'll get to in a moment, No, it doesn't, because the problem isn't really a rules problem.
The thing is, the whole "Murderhoboes" problem isn't encoded in the rules - it's due to a common misinterpretation of the rules, and one that goes back all the way to AD&D 1E, coupled to a lack of mechanical resolution options.
There's no requirement to kill opponents to get the XP for defeating them. If you drive them off or negotiate them off, you still get the full XP for the encounter in almost every D&D rule set since 1978.
Even in Holmes, it's not just kill:
D&D has always allowed for non-violent "overcoming" of monsters.
This hasn't changed in any edition since Holmes.
It explicitly hasn't been done away with in D&D Next Basic - from Basic DMG v0.1, p.5:
The issue arises from it being easier to kill than capture by force (which is actually not unrealistic), and from no mechanical way to overcome by talk, excepting Comeliness 25+ characters in AD&D 1.5 (AD&D 1 + UA).
Essentially, the problem arises not from the rules, but from the nature of people... who tend to do what there are rules for doing more than what the GM has to invent or make wild judgements about.
Not really. And at this point it certainly does it less well than 4e did. However, we only have Basic, so it may improve as we see the DMG.
This is in marked contrast to 4e's description which used the verbiage "overcome" and took a more nuanced approach describing it in several paragraphs to talk about what "overcoming" a challenge means (Though to be honest, 90% of the time, 4e, like 3.5 devolves into muder hobodom, so how meaningful this section is should be up for debate).
So while 5e leaves room for 4e's nuance, it seems clear that it's default mode is muderhobo.
In the D&D Starter Set the included adventure, The Lost Mine of Phandelver, explicitly includes XP for completing significant tasks. Also includes the award of XP for resolving a encounter rather just for outright killing.
from Page 24 of the Lost Mine of Phandelver
My opinion is that the award for killing monsters is only a part of a larger system of awarding XP. This is based on reading the various Legend Lord articles on what yet to come the recently released D&D 5e Basic DM Guidelines, and two adventures that been released so far.