解:$(1) $原式$=(2 + 1)(2 - 1)(2^2 + 1)(2^4 + 1)(2^8 + 1)(2^{16} + 1)$
$=(2^2 - 1)(2^2 + 1)(2^4 + 1)(2^8 + 1)(2^{16} + 1)$
$=(2^4 - 1)(2^4 + 1)(2^8 + 1)(2^{16} + 1)$
$=(2^8 - 1)(2^8 + 1)(2^{16} + 1$
$=(2^{16} - 1)(2^{16} + 1)$
$=2^{32} - 1$
$(2) $原式$=(5 + 1)(5 - 1)(5^2 + 1)(5^4 + 1)(5^8 + 1)(5^{16} + 1)×\frac {1}{5 - 1}$
$=(5^2 - 1)(5^2 + 1)(5^4 + 1)(5^8 + 1)(5^{16} + 1)×\frac {1}{5 - 1}$
$=(5^4 - 1)(5^4 + 1)(5^8 + 1)(5^{16} + 1)×\frac {1}{4}$
$=(5^8 - 1)(5^8 + 1)(5^{16} + 1)×\frac {1}{4}$
$=(5^{16} - 1)(5^{16} + 1)×\frac {1}{4}$
$=(5^{32} - 1)×\frac {1}{4}$
$=\frac {5^{32} - 1}{4}$