- Generally accepted explanation of the observed accelerated expansion of the present day universe is based on the idea of the existence of a new entity called dark energy. Resolution of the 'cosmic coincidence' problem implies that dark energy and dark matter follow the same scaling solution during a significant period of evolution. This becomes possible only if there exists a coupling of the dark energy (modeled by a light scalar field) to dark matter. This conclusion following from the observed cosmological data serves for an additional evidence of well-known theoretical predictions of a light scalar coupled to matter. However, according to the results of the fifth force experiments, a similar coupling of the light scalar field to visible (baryonic) matter is strongly suppressed. After a brief review of some models intended for resolution of this 'fifth force problem', we present a model with spontaneously broken scale invariance where the strength of the dilaton-to-matter coupling appears to be dependent on the matter density. This is realized without any special assumptions in the underlying action intended for obtaining such a dependence. As a result the dilaton-to-matter coupling constant measured under conditions of all known fifth force experiments turns out automatically (without any sort of fine tuning) to be so small that, at least in the near future, experiments will not be able to reveal it. On the other hand, if the matter is very diluted (such as galaxy halo dark matter) then its coupling to the dilaton may not be weak. However, the latter situation is realized under conditions not compatible with the design of the fifth force experiments.