It is common to use notes that are not in the scale to add color. It's called chromaticism, from the ancient Greek word for color.
Think how composers use a G# instead of a G in A minor, for example as a part of an E chord. A semitone creates more tension and the tendency of G# to resolve to (go to) A is more powerful. This is called a chromatic approach note. But since this particular usage is very common, we usually label it the "harmonic minor scale".
Similarly, using an F# to avoid the melodically awkward (to western classical ears) augmented second between F and G# is also quite common. Then we label it as the "melodic minor" scale.
These two so-called alterations are very common to warrant a new name. But there are many other possibilities.
The D# here is a quite common example. It's a chromatic approach note to E. A few notes later Beethoven uses a D natural, notice how that strong tendency of resolving to E is now mostly gone.
The reason it's labeled D#, instead of Eb is this. It's not a flattened fifth, it's a sharpened fourth. The fifth (E) is still there, this one is a degree lower, so it's a (sharpened) fourth. A flattened fifth (Eb) would replace the E and would tend to resolve to D, because just like the sharpened notes tend to resolve upwards, flattened notes tend to resolve downwards.
Granted, it mostly concerns classical music. Blues is a different beast. The flattened fifth and sharpened fourth can be used interchangeably. The convention is still to notate them with a sharp for upward moving lines and with a flat for downward moving lines but it's not used consistently.
That blue note, after all, does not even exist on a piano when properly played or sung. It's generally flatter than D#/Eb when sung or played on a fretless instrument or on an instrument that can do bends. It's an alien coming from a different musical culture, a square peg that we try to squeeze in to the round hole we have: The so-called equal temperament.