Analyzing the Expression: -3 + | -4 + 8 |-5 + | a | < 0

To solve this problem, we'll simplify and evaluate the absolute value expressions:

Firstly, simplify the inner part of the nested absolute mixed with constants:
Calculate each absolute:
$|-4 + 8| = |4| = 4$. This uses basic absolute value rules.

Subsequently, substitute back into initial inequality:
$|-3 + 4 - 5| + |a| < 0$. Simplify by arithmetic: $|-3 + 4 - 5| = |-4| = 4$. Thus, the expression turns to $4 + |a| < 0$.

The expression can never be less than zero, because:

• Since $|a|$ returns non-negative results.
• The total sum of terms $4 + |a|$ is always $\geq 4$, clearly contradicting the inequality demand that this whole larger structure must become negative.

Therefore, the expression $|-3 + |-4 + 8| - 5 | + |a| < 0$ has No solution because it’s impossible under real number and absolute value rules.