The $5S_{1/2}rightarrow 5D_{5/2}$ two-photon transition in Rb is of interest for the development of a compact optical atomic clock. Here we present a rigorous calculation of the 778.1~nm ac-Stark shift ($2.30(4) times10^{-13}$(mW/mm$^2$)$^{-1}$) that is in good agreement with our measured value of $2.5(2) times10^{-13}$(mW/mm$^2$)$^{-1}$. We include a calculation of the temperature-dependent blackbody radiation shift, we predict that the clock could be operated either with zero net BBR shift ($T=495.9(27)$~K) or with zero first-order sensitivity ($T=368.1(14)$~K). Also described is the calculation of the dc-Stark shift of 5.5(1)$times 10^{-15}$/(V/cm$^2$) as well as clock sensitivities to optical alignment variations in both a cats eye and flat mirror retro-reflector. Finally, we characterize these Stark effects discussing mitigation techniques necessary to reduce final clock instabilities.
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