"set their clocks 5 Minutes Fast"

The earths rotation is actually 23 hours, 56minutes, 4 seconds.

From Wikipedia: Earths rotation


Stellar and sidereal day
On a prograde planet like the Earth, the stellar day is shorter than the solar day. At time 1, the Sun and a certain distant star are both overhead. At time 2, the planet has rotated 360° and the distant star is overhead again but the Sun is not (1→2 = one stellar day). It is not until a little later, at time 3, that the Sun is overhead again (1→3 = one solar day).

Earth's rotation period relative to the fixed stars, called its stellar day by the International Earth Rotation and Reference Systems Service (IERS), is 86,164.098 903 691 seconds of mean solar time (UT1) (23h 56m 4.098 903 691s, 0.997 269 663 237 16 mean solar days).[11][n 2] Earth's rotation period relative to the precessing or moving mean vernal equinox, misnamed its sidereal day,[n 3] is 86,164.090 530 832 88 seconds of mean solar time (UT1) (23h 56m 4.090 530 832 88s, 0.997 269 566 329 08 mean solar days).[11] Thus the sidereal day is shorter than the stellar day by about 8.4 ms.[13]

Both the stellar day and the sidereal day are shorter than the mean solar day by about 3 minutes 56 seconds.