  Experimental searches for new, "fifth" forces are attracting a lot of
attention because they allow to test theoretical extensions to the standard
model. Here, we report a new experimental search for possible fifth forces,
specifically spin-and-velocity dependent forces, by using a K-Rb-$^{21}$Ne
co-magnetometer and a tungsten ring featuring a high nucleon density. Taking
advantage of the high sensitivity of the co-magnetometer, the pseudomagnetic
field from the fifth force is measured to be $<7$\,aT. This sets new limits on
coupling constants for the neutron-nucleon and proton-nucleon interactions in
the range of $\ge 0.1$ m. The coupling constant limits are established to be
$|g_V^n|<6.6\times 10^{-11}$ and $|g_V^p|<3.0\times 10^{-10}$, which are more
than one order of magnitude tighter than astronomical and cosmological limits
on the coupling between the new gauge boson such as Z$'$ and standard model
particles.
