Enneagram five is usually view as the land of introverts. ENTp is the only sociotype that (to some degree) is usually accepted as E5 capable. Some people even suggest ENTj as a remote possibility. In my opinion, none of them should be valid. Regardless how well balanced a particular extrovert could be.
The core of E5 implies that the subject tends to withdraw from the external world (introversion). If "left alone", this natural impulse predates most of the behavior causing the user becomes unbalanced (as happens with all enneagrams). But my point is that this "harmful trend" which the user should learn to compensate, is natural to this personality. Given any E5 subject, most of the time this should be counterbalanced instead of forced.
This is not compatible with extroversion. Sure any extrovert could be pensive, reclusive and such, but this is not the natural trend. Extroverted functions are "broad" whereas introverted ones are "deep" for the same area of work. Where an intellectual extrovert would want more (quantity: information, theories, whatever) an introverted one would want better (quality). Seeking the deepest truth is much more an introverted thing. Obviously introversion, as a behavioral characteristic, is not black/white. All intermediate points should be possible, but if someone is in the middle, there's no reason for calling him/her ILE istead of LII...
I think the idea that ILEs can be E5 originates in the common association E5=intellectual, thinker. Most ILEs whould describe themselves as such, and also they're seen in this way by others. But being an "intellectual" does not imply E5, it's required something more: a certain motivation. This motivation, in the case of ILEs, fits much better in E7. The E5 mimicking is caused by an internalization of the desired object, instead a real detachment from it (E5 requisite). ILEs are Ti egos, and Ti (despite all of its potential) has certain trend to reify ideas, which are almost seen as "real objects". The detachment required for being an E5 is not really happening. While playing (E7, broad, quantity) with this imaginary objects, interaction with real physical world is almost not required. The more you play the less you interact (intuition helps here, but not a requisite).
I have doubts about the validity of interrelationships between enneagrams, but if we accept them, ILE+E5 becomes even more improbable. E5 degenerates in the path to E7. If we could associate a single function to an enneagram, E7 and Ne are a very good match. So do ILEs degenerate as they become closer to their leading function, the core of their psyche??? Well Jung said that emphasizing too much the first function causes unbalance. But LIIs as crea-Ne, they achieve balance through Ne. LII positive development should be then in the direction of E7, instead being this a degenerative pathway...
There's a famous case that makes people predisposed for accepting this combination: Eintein, who is commonly typed as ILE, and also commonly typed as E5. A "genius"must belong to "genius types", right?
Being an ethical extrovert and also a E5 makes no sense, methinks. I've seen some people typing themselves as such, and probably they do this because (again) they consider themselves as intellectuals. Guys and/or girls, being an E5 does not make you more intellectual, more intelligent, or being more right, so there's no need to force such combination. I could see (unlikely but not impossible) IF+E5, but EF+E5? No way.