From Förberedande kurs i matematik 2

We calculate what the expression will be

\displaystyle (2-i)+(5+3i) = 2+5+(-1+3)i = 7+2i

and then calculate the magnitude,

\displaystyle |7+2i| = \sqrt{7^2+2^2} = \sqrt{49+4} = \sqrt{53}\,\textrm{.}

Note: It is not possible to calculate the magnitude of the terms individually

\displaystyle |(2-i)+(5+3i)| \ne |2-i| + |5+3i|\,\textrm{.}