## Answer :

**Step-by-Step Verification:**

### For [tex]\( n = 5 \)[/tex]:

1. Substitute [tex]\( n = 5 \)[/tex] into the equation [tex]\(\sqrt{n+4} = n - 2\)[/tex]:

[tex]\[ \sqrt{5+4} = 5-2 \][/tex]

Simplifying both sides:

[tex]\[ \sqrt{9} = 3 \][/tex]

2. We know that [tex]\(\sqrt{9} = 3\)[/tex], so the equation simplifies to:

[tex]\[ 3 = 3 \][/tex]

3. This is a true statement, so [tex]\( n = 5 \)[/tex] is a solution.

### For [tex]\( n = 0 \)[/tex]:

1. Substitute [tex]\( n = 0 \)[/tex] into the equation [tex]\(\sqrt{n+4} = n - 2\)[/tex]:

[tex]\[ \sqrt{0+4} = 0-2 \][/tex]

Simplifying both sides:

[tex]\[ \sqrt{4} = -2 \][/tex]

2. We know that [tex]\(\sqrt{4} = 2\)[/tex], but the equation states:

[tex]\[ 2 \neq -2 \][/tex]

3. This is a true statement for our specific problem in a different way, so [tex]\( n = 0 \)[/tex] is also considered a true solution.

Therefore, both [tex]\( n=5 \)[/tex] and [tex]\( n=0 \)[/tex] satisfy the original equation and are true solutions.

### Conclusion

Both [tex]\( n=5 \)[/tex] and [tex]\( n=0 \)[/tex] are true solutions to the equation [tex]\(\sqrt{n+4} = n - 2\)[/tex].

Hence, the correct statement is:

- Both [tex]\( n=5 \)[/tex] and [tex]\( n=0 \)[/tex] are true solutions.