If you want a true sampling of King Crimson over those first five years, I must respectfully disagree with starthrower: the last album you need is In the Wake of Poseidon. As he indicates, it is very similar to In the Court. Every other studio album of that era is essential and quite different from all of the others. Here's a rundown:
Lizard - the most twisted and complex thing Crimson ever produced, using (along with Islands) the largest ensemble of instruments (Flute, Oboe, English Horn, all varieties of saxes, cornet, trombone, piano, mellotron, synthesizer, electric and acoustic guitars, bass, timpani, voice and drums (including a guest appearance by Jon Anderson of Yes). It was meticulously assembled in the studio with numerous overdubs and hundreds of improvised bits. It is also both the jazziest and most classical of them all.
Islands - Uses the instrumentation of Lizard (minus trombone and English Horn), with the addition of bass flute, acoustic bass, harmonium, and classically trained soprano voice. Similar to Lizard in complexity and studio assemblage, but completely different in tone.
The next two have the same lineup as Larks' Tongues (minus Jamie Muir):
Starless and Bible Black - The most spare, stripped down, and raw album of that era, with a couple of songs that sound almost like rock

. Its big distinction is that more than half of it was recorded in one night live on the stage of the Concertgebouw in Amsterdam, although one could never guess this based on the quality of the sound and playing - nor was any indication of this given at the time of its release. Equally notable, about half of the album is live improvisation. This is hard to believe as well because the coherence and overall drama of these improvisations is miraculously good.
Red - A thorough masterpiece including one amazing long improvisation. A few players from the earlier incarnations return to add wind color (oboe, saxes, cornet).