For a complex number $z,$ compute the minimum value of
\[|z + 5 - 3i| + |z - 7 + 2i|.\]
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
For a complex number $z,$ compute the minimum value of
\[|z + 5 - 3i| + |z - 7 + 2i|.\]
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
13
For a complex number $z,$ compute the minimum value of
\[|z + 5 - 3i| + |z - 7 + 2i|.\]
train