my $byte = 129;                          # 0b10000001 = 129
my $most_significant_5  = $byte >> 3;    # 0b10000    =  16
my $least_significant_3 = $byte & 0x7;   # 0b     001 =   1
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How did I arrive at that? Basically, you want to either

• Mask out the bits of higher significance than those you want, then shift the bits you want to index 0; or
• Shift the bits you want to index 0 then mask out the bits of higher significance than those you want.

                             is a simplification of
              ----------------------------------------------------
$byte >> 3    ( $byte & 0xFF ) >> 3    or    ( $byte >> 3 ) & 0x1F
$byte & 0x7   ( $byte & 0x7  ) >> 0    or    ( $byte >> 0 ) & 0x7
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Notes;

• «0x7» is 0b111 or 2³-1. «& 0x7» "keeps" only the least significant 3 bits.
• «0x1F» is 0b11111 or 2⁵-1. «& 0x7» "keeps" only the least significant 5 bits.
• «0xFF» is 0b11111111 or 2⁸-1. «& 0x7» "keeps" only the least significant 8 bits.
• «& 0xFF» is a no-op when dealing with 8-bit values.
• «>> 0» is a no-op for integers, which is what we're dealing with.