Five, a positive integer, if each of its prime factors is at least double (i.e., the exponent of each prime factor is no less than 2), then the positive integer is called a "beautiful number." If two consecutive positive integers are both "beautiful numbers," they are called a pair of "twin beautiful numbers." For example, 8 and 9 are a pair of "twin beautiful numbers." Please find two more pairs of "twin beautiful numbers."
Five, Solution Given that $(8,9)$ is a pair of “twin beautiful numbers”.

Let $(n, n+1)$ be a pair of “bent beautiful numbers”. From this, we know that $4 n(n+1)$ is also a beautiful number.
And $4 n(n+1)+1=4 n^{2}+4 n+1=(2 n+1)^{2}$ is a perfect square, which is easily known to be a beautiful number.

Therefore, $(4 n(n+1), 4 n(n+1)+1)$ is a pair of “twin beautiful numbers”.
Thus, from $n=8$ we know
\[
\begin{array}{l}
4 n(n+1)=4 \times 8 \times 9=288 . \\
4 n(n+1)+1=289 .
\end{array}
\]

Hence, $(288,289)$ is a pair of “twin beautiful numbers”.
Taking $n=288$, then
\[
\begin{aligned}
4 n(n+1) & =4 \times 288 \times 289=332928 \\
( & \left.=2^{7} \times 3^{2} \times 17^{2}\right), \\
4 n(n+1) & +1=332929=(577)^{2} .
\end{aligned}
\]

Therefore, (332928, 332929) is another pair of “twin beautiful numbers”.