To find the fifth term of the geometric sequence given (5, 15, 45,...), we first identify the common ratio.
The first term \( a_1 = 5 \). The second term \( a_2 = 15 \). The third term \( a_3 = 45 \).
To find the common ratio \( r \), we can divide the second term by the first term:
\[ r = \frac{a_2}{a_1} = \frac{15}{5} = 3 \]
We can also verify this with the third term:
\[ r = \frac{a_3}{a_2} = \frac{45}{15} = 3 \]
So, the common ratio is \( r = 3 \).
Now, we can find the subsequent terms using the formula for the \( n \)-th term of a geometric sequence:
\[ a_n = a_1 \cdot r^{(n-1)} \]
For the fifth term \( a_5 \):
\[ a_5 = a_1 \cdot r^{(5-1)} = 5 \cdot 3^4 \]
Calculating \( 3^4 \):
\[ 3^4 = 3 \cdot 3 \cdot 3 \cdot 3 = 81 \]
Now substitute back:
\[ a_5 = 5 \cdot 81 = 405 \]
Thus, the fifth term of the geometric sequence is \( 405 \).
Therefore, the answer is:
405