Escaping from a problem (mark where it's correct)

The answer is:

HARRY HOUDINI, the renowned escape artist (hence the title) and stunt performer.

How to work this out? First focus on all the numbers:

If we consider the positions of the five digits to be numbered 1, 2, 3, 4 and 5 (from left to right), we should then assign a '1' in the corresponding square bracketed box below if the number in that position equals that position's number (i.e. if a '1' is in position 1, a '2' is in position 2, etc.) and a '0' otherwise. This yields the following (square boxes concatenated into a single string):

VCIMB YUNFS XHDHU GRNSW
(43125) (42531) (21345) (51324)
[00001] [01000] [00111] [00100]

OLMVD MEYIT SGVUW XCSAR
(24135) (42135) (21543) (51342)
[00001] [01001] [00010] [00110]

We can then...

Treat these square-bracketed numbers as binary strings to produce the numbers:

[1][8][7][4]
and
[1][9][2][6]

Now, focus on the letters:

If we also extract the letters that fall in the same positions within the strings as the matching numbers, we can extract something of use:

VCIMB YUNFS XHDHU GRNSW
OLMVD MEYIT SGVUW XCSAR

i.e. BUDHUN and DETUSA

Putting this all together, we have:

1874 BUDHUN and 1926 DETUSA. When we interpret 'BUDHUN' as 'Budapest, Hungary' and 'DETUSA' as 'Detroit, USA', this looks an awful lot like a birth date and birthplace and a death date and... er... deathplace.

In other words, we are likely looking for the 12-letter name of an individual who was born in 1874 in Budapest, Hungary, and died in 1926 in Detroit, USA.

And possibly the most famous person who fulfils these criteria (and the first hit on a Google search) is HARRY HOUDINI, a man whose profession suits the choice of words in the title perfectly!