  Cosmological probes at any redshift are necessary to reconstruct consistently
the cosmic history. Studying properly the tension on the Hubble constant,
$H_0$, obtained by Supernovae Type Ia (SNe Ia) and the Planck measurements of
the Cosmic Microwave Background Radiation would require complete samples of
distance indicators at any epoch. Gamma-Ray Bursts (GRBs) are necessary for the
aforementioned task because of their huge luminosity that allows us to extend
the cosmic ladder at very high redshifts. However, using GRBs alone as standard
candles is challenging because their luminosity varies widely. To this end, we
choose a reliable correlation for GRBs with a very small intrinsic scatter: the
so-called fundamental plane correlation for GRB afterglows corrected for
selection biases and redshift evolution. We choose a well-defined sample: the
platinum sample, composed of 50 Long GRBs. To further constrain cosmological
parameters, we use Baryon Acoustic Oscillations (BAOs) given their reliability
as standard rulers. Thus, we have applied GRBs, SNe Ia, and BAOs in a binned
analysis in redshifts so that GRBs' contribution is fully included in the last
redshift bin, which reaches $z=5$. We use the fundamental plane correlation
together with SNe Ia and BAOs, to constrain $H_0$ and the density matter today,
$\Omega_{M}$. This methodology allows us to assess the role of GRBs combined
with SNe Ia and BAOs. We have obtained results for $H_0$ and $\Omega_{M}$ using
GRBs+ SNe Ia+BAOs with better precision than the SNe Ia alone for every bin,
thus confirming the beneficial role of BAOs and GRBs added together. In
addition, consistent results between GRBs+ SNe Ia +BAOs are obtained when
compared with the SNe Ia +BAOs, showing the importance of GRBs since the
distance ladder is extended up to $z=5$ with a similar precision obtained with
other probes without including the GRBs.
