Taken from the documentation, you have the following axioms:
if a string is 0-55 bytes long, the RLP encoding consists of a single byte with value 0x80 plus the length of the string followed by the string. The range of the first byte is thus [0x80, 0xb7].
If the total payload of a list (i.e. the combined length of all its items being RLP encoded) is 0-55 bytes long, the RLP encoding consists of a single byte with value 0xc0 plus the length of the list followed by the concatenation of the RLP encodings of the items. The range of the first byte is thus [0xc0, 0xf7].
Hence, ["cat",[],"pig",[""],"sheep"] would be encoded with the following logic:
You would encore cat like
0x83, 'c', 'a', 't'
"cat" is a string, hence you start from 0x80 and add the length of the string (3) so it gives us 0x83, then the characters of the string.
[] would be
This array contains ONE empty array.
As 0xc1 is the length of the array (the array contain one element, here  ), and 0xc0 is the length of the second array (empty element)
"pig" is same as "cat", a string of 3 characters so:
0x83, 'p', 'i', 'g'
[""] is an array of ONE element being an empty string (0 characters) so it would encode as
0xc1, 0x80 (0xc0 + 1 , 0x80 + 0)
"sheep" is a 5 characters string, so it would encode as:
0x85, 's', 'h', 'e', 'e', 'p' (0x80 + 5, and each letter of the string)
The whole array contains 18 bytes of value, so it would encode as:
[ 0xd2, 0x83, 'c', 'a', 't', 0xc1, 0xc0, 0x83, 'p', 'i', 'g', 0xc1, 0x80, 0x85, 's', 'h', 'e', 'e', 'p'] (0xd2 is 0xc0 + 0x12, 0x12 being 18 in decimal)
For clarity purpose, characters have not been encoded in hexadecimal, but the real encoding will look like this:
[0xd2, 0x83, 0x63, 0x61, 0x74, 0xc1, 0xc0, 0x83, 0x70, 0x69, 0x67, 0xc1, 0x80, 0x85, 0x73, 0x68, 0x65, 0x65, 0x70]