That's an old song, I think.
To understand the phrase, you should note that the five colors (red, black, blue, yellow and white) represent Five Elements. Affected by religions such as Taoism and Buddhism, Korean shamanism also uses five colors (red, green, blue, yellow and white).
To keep it simple, I'd say those strings or similar things (flags, ribbons, etc.) in Korean shamanism are used as talismans believed to bring good luck.
I couldn't find any photos of fishing boats with colored strings. For now, I guess 오색실 refers to the flags called 오색기. They will look like threads or strings if you see them from a distance. Locals in Korea will agree that 오색기 does not sound lovely. The word, 오색실, is much better to describe something beautifully. This is a probable reason the lyricist used 오색실.
But after reading a few comments, I've thought 오색실 may refer to the fishnet. If its threads under the setting sun are compared to a rainbow, the word choice sounds quite plausible. 오색 means not only five colors but also all colors existing in the universe. You can find such a world view from many words and phrases: 오색선, 오색등, 오색구름, 오색 단풍, 오색 풍선, 오색영롱, 오색찬란...
오색천 (Five-Colored Ribbons) (Encyclopedia of Korean Folk Culture)
Photos: five-colored flags with fishing boats (1) (2)