  We construct $ 1/2 $ BPS 1-instanton states in the Hilbert space of $ 5d $
gauge theories. The states are local with the scale size $ \rho=0 $. With the
degeneracy from the gauge orientation taken into account, the BPS spectrum
consists of an infinite number of states in the definite representations of the
gauge group and the $ (J,0) $ representation of the $ SO(4)\cong SU(2)_{L}
\times SU(2)_{R} $ rotation group. In the brane webs realization of the $ 5d $
$ \mathcal{N}=1 $ gauge theory, BPS states are string webs inside the 5-brane
webs. For a theory with the gauge group $ SU(N) $ and the Chern-Simons level $
\kappa $, we give a classification of string webs in the Coulomb branch and
show that for each web, one can always find an instanton state carrying the
same spin and the same electric charge. The action of supercharges on instanton
states gives the instanton supermultiplets. For the $ \mathcal{N} =1$ $ SU(2) $
gauge theory with $ N_{f} \leq 4$, we construct the instanton vector and hyper
multiplets, which, together with the original multiplets of the theory, furnish
the complete representation of the $ E_{N_{f}+1} $ group at UV.
