Alex is on Earth and the planet Flez is 5 light years away. Glen, is on a spaceship approaching Earth at $0.8$c along a direct path towards Flez. Unfortunately Flez explodes. According to Alex, this occurred two years after Glen passed Earth. Call the passing of Glen's spaceship past Alex on Earth time zero for both.
According to Glen, how far is his spaceship from Flez when it explodes?
At what time does it explode, according to Glen?
So I know if I use Lorentz transformation I get the following:
$$x_2' = \frac{x_2-vt_2}{\sqrt{1-\frac{v^2}{c^2}}} = 1.666*(5\text{ly} - 0.8*2\text{yr}) = 5.7\text{ light year}$$
which is the correct answer but I don't understand conceptually why Glen is still $5.7$ light years away from the planet Flez? How is it that Glen still hasn't reached Earth when the planet Flex explodes when we already stipulated that the explosion happened two years after Glenn passed Earth in Alex reference frame?
Also, the time it explodes according to Glen will be $-3.3$ years, which is also confusing me.
This sort of thing is perhaps best understood using a Minkowski diagram:
The unprimed coordinate system is Alex’s, with Earth at rest; the primed coordinate system is Glen’s, with the spaceship at rest. The vertical lines are the world line of the Earth (which coincides with the $t$ axis) and the world line of Flez (and its debris). The $t'$ axis is the world line of the spaceship. The $x'$ axis is the set of events that are simultaneous with the passing in the primed coordinate system. You can see that the $t'$ coordinate of the explosion is negative. Here $c=1$ and $1\text{ ly}=1$, so the distance from Earth to Flez is $5$, the $t$ coordinate of the explosion is $2$, and the slope of the $x'$ axis is $0.8$.
I suspect that your confusion arises from a residual tendency to think of simultaneity (and thus of temporal order) as absolute:
The crucial point here is “in Alex’ reference frame”. The fact that the explosion happens after the passing in one reference frame doesn’t imply that it does so in all reference frames. Lorentz transformations perserve the causal order of events (i.e. they don’t change whether $A$ is inside, outside or on $B$’s light cone); but they don’t preserve the temporal order of events that are outside each other’s light cones (i.e. they may change whether $A$ happened before, after or at the same time as $B$). In fact, for any two events $A$ and $B$ that are outside each other’s light cones (and thus cannot influence each other causally), there are Lorentz transformations that make them occur in either order, or simultaneously.
You may also want to reflect on how you used the word “when” in the sentence above: “when the planet Flez explodes” sounds a bit as if there is some fixed time at which this occurs. (This misguided idea is of course firmly ingrained in our everyday language, which is modeled on the absoluteness of simultaneity.)