The equation of the given line is:

x+3

3

=

4−y

5

=

z+8

6

.
i.e.,

x+3

3

=

y−4

−5

=

z+8

6

The required line is parallel to the given line. Therefore, direction ratios of the required line are same as the direction ratio of the given line. So, the direction ratios of the required line are 3, -5, and 6.
Thus, the equation of the straight line passing through (-2, 4, -5) and having direction ratios 3, -5, 6 is

x−(−2)

3

=

y−4

−5

=

z−(−5)

6

i.e.,

x+2

3

=

4−y

5

=

z+5

6