  We rewiew and scrutinize the existing mass determinations of the pentaquarks
from the exponential Laplace Sum Rules (LSR). We do not find any sum rule
window for extracting optimal and reliable results from the LSR, due to the
unusual slow convergence of the OPE and to the exceptional important role of
the QCD continuum into the spectral function in this channel. Instead, we use
in this channel,for the first time, Finite Energy Sum Rules (FESR), which
exhibit a nice stability in the QCD continuum threshold t_c, at which one can
extract, with a good accuracy, the mass of the lowest resonance. Including the
D=7, 9 condensate contributions in the OPE, we obtain M_Theta=(1513+- 114) MeV,
and the corresponding residue lambda_Theta^2= -(0.14-- 0.49)x 10^{-9} GeV^{12},
which favours the I=0, J=1/2, and negative parity S-wave interpretation of the
Theta (1540). However, our analysis indicates a degeneracy between the unmixed
I=0 and I=1 S-wave states. In the I=0, J=1/2, P-wave channel, we obtain, for
the P-resonance, M_P = (1.99+- 0.19) GeV and lambda_P= -(0.7--7.1)x 10^{-9}
GeV^{14}, which we expect to be discovered experimentally. Our results also
suggest that some intuitive choices of the continuum threshold used in the LSR
literature are inconsistent with the FESR results. Finally, a study of the
Theta-K-N coupling using a vertex sum rule shows that, for the I=0, S-wave
channel, the leading OPE contributions only start to order alpha_s^2 in the
chiral limit m_s=0, indicating that the Theta is very narrow.
