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We report the measurement of the hyperfine splitting in the $7D_{5/2}$ stateof $^{133}$Cs using high resolution Doppler-free two-photon spectroscopyenabled by precise frequency scans using an acousto-optic modulator. All thesix hyperfine levels are resolved in our spectra. We determine the hyperfinecoupling constants A = -1.70867(62) MHz and B = 0.050(14) MHz which representover 20-times improvement in the precision of both A and B. Moreover, ourmeasurement is sufficiently precise to put bounds on the value of the magneticoctupole coupling constant C = 0.4(1.4) kHz for the $7D_{5/2}$ state. Weadditionally report the measurement of ac Stark shift [-46 $\pm$ 4Hz/(W/cm$^2$)], collisional shift and pressure broadening which are importantfor optical frequency standards based on the $6S_{1/2} \rightarrow 7D_{5/2}$two-photon transition.

Hyperfine coupling constants of the cesium $7D_{5/2}$ state measured up to the octupole term