To find the length of \( TE \) in triangle \( NTE \) given that it is similar to triangle \( KLA \), we can use the property of similar triangles that states the ratios of corresponding sides are equal.
From the problem, we know:
- \( LA = 8 \)
- \( EN = 125 \)
- \( AK = 5 \)
First, we find the ratio of the corresponding sides from triangles \( KLA \) and \( NTE \). Since \( KLA \) and \( NTE \) are similar, we can denote:
\[ \frac{LA}{AK} = \frac{EN}{TE} \]
Substituting the known values into this relationship, we have:
\[ \frac{8}{5} = \frac{125}{TE} \]
Now, to solve for \( TE \), we can cross-multiply:
\[ 8 \times TE = 125 \times 5 \]
Calculating \( 125 \times 5 \):
\[ 125 \times 5 = 625 \]
So we have:
\[ 8 \times TE = 625 \]
Now, divide both sides by 8 to solve for \( TE \):
\[ TE = \frac{625}{8} \]
Calculating this gives:
\[ TE = 78.125 \]
Thus, the length of \( TE \) is \( \boxed{78.125} \).