To see how a king (or high noble) surrounded by advisors (or lesser nobles) is a balanced is a troublesome task at best. Let's look at some, but not all the dynamics that could influence the adventures in play:
What makes a king?
Traditionally in antics and early medieval times there are several pillars that a king has to hold on to to stay king:
- godly investiture / divine right of kings
- proof of power
Lineage is something that either is or isn't (and if it isn't, it will be corrected for history), the divine right of kings is given by clergy pretty much, stays the proof of power. This proof of power is not only what makes the king in the antics, it is what keeps him in power.
When a problem emerges his vassals can't handle on their own, the king is obligated to go and deal with it. This blows up the conflicts the king (or his troops) will have to face, but it drives him from crisis to crisis (aka: adventure to adventure).
Historical example: One of 4 possible Macedon kings manages to ally enough people to back his claim to the throne, then he levies troops from all of Greece and goes to march against Persia. And then march on. And on. Until he loses the back up of his troops and returns to Persepolis... and die of fever. All the time he was surrounded by his best buddies since childhood, all of them equally capable.
His personal levies and honor guard will be large though... He might have to be a frontline king by tradition and he has to prove he is better than any of his troops to cement his proof of power and divine investiture. Being 5 levels behind the group will make this very hard, he might actually need to be very close to the level of his Hetairoi (Companions), maybe even outshine them by half a level in this case though.
Who's actually in charge?
I know, we often like to think a King is the one and only thing that can trample over laws, dictate what is going on and in any way 'allmighty' and absolute as long as it is mundane power... but he isn't. A king just as much needs his regal council of ministers and advisors to stay informed about the stuff that matters as well as to outsource routine business.
In a feudal society, these advisors are somewhat lesser landed nobles than the king (which can still be high nobility), but also clergy and well known studied people (like mages and physicians) do flock to a court, as do of course courtiers, representatives from powerful groups and so on. Now, They take some of the tedious tasks away, but they also get their share of power this way. Think of the power of a king as a cake: To get somebody to do parts of your job, they want a slice of it. So the king has to carve out special privileges to these people he needs tp run the country...
Now: How many privileges like tax exemption or the right to approve of a king did he or his lineage before him hand out? The less absolute he is, the less the king matters but as a representative figure (see modern Scandinavia or Britain). If the king himself is not much more than the nominal head of state, him going off to an adventure might be not only ok with the council but also expected, to keep him busy and off the books.
How about the weak king's honor guard?
Of course he will have his honor guard of maybe a few hundred, but that is just one battalion while the kingdom itself could field a legion - he is no threat. And then there are of course provisions that keep him from taking too many of these vets with him: The only group that is allowed to guard the palace is the same honor guard he can count on to take out to adventure. So most of his personal troops are most often bound, but he can take a handful of his vets with him. In the field against banditry and highwaymen his 20-such soldiers are a force to be reckoned with, but against dragons they don't do a dent. But then again, how easily do bandits that have a charismatic leader flock to a common course (all the moneys for us)?
So: Scale up banditry a notch. Instead of 5-10 highwayman, it's an outright bandit encampment that has to be taken out, about 30 robbers with 5 leaders (as enemies for the core group).
The other players?
In this case of a weak monarch, the other players easily can be just the noble best buddies or advisors that likewise are merely figureheads to their branches. Cutting the King in levels a bit compared to his buddies/advisors might be explained by him being younger than them, but keep in mind he should be somewhat capable in comparison to them, not only be a utility character. 5 Levels strike me crippling, 1-2 levels might be within the bounds much easier.
The Court as playground
We just explored what might make a king powerful or cut the power of the king down to a lower level, but what if the physical power of the king doesn't matter at all? After all an absolute king is much more a statesman than a warrior. He handles intrigues, deals with foreign powers on a huge scale and... doesn't get to delve into dungeons. Sorry, intrigue play isn't the strength of D&D.