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The differential cross section for the process p(e,e{prime}p) {eta} has been measured at Q{sup 2} {approx} 5.7 and 7.0(GeV/c){sup 2} for center-of-mass energies from threshold to 1.8 GeV, encompassing the S{sub 11}(1535) resonance, which dominates the channel. This is the highest momentum-transfer measurement of this exclusive process to date. The helicity-conserving transition amplitude A{sub 1/2}, for the production of the S{sub 11}(1535) resonance, is extracted from the data. Within the limited Q{sup 2} now measured, this quantity appears to begin scaling as Q{sup -3} - a predicted, but not definitive, signal of the dominance of perturbative QCD at Q{sup 2} {approx} 5 (GeV/c){sup 2}.