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In the framework of a five-dimensional(5D)bounce cosmological model,a useful function f(z)is obtained by giving a concrete expression of deceleration parameter q(z)=q1+q2/1+1n(1+z).Then usng the obtained Hubble parameter H(z)according to the function f(z),we constrain the accelerating universe from recent cosmic observations:the 192 ESSENCE SNe Ia and the 9 observational H(z)data.The best fitting values of transition redshift zT and current deceleration parameter q0 are given as zT=o.65±0.25-0.12 and q0=-0.76+0.15-0.15(1σ).Furthermore,in the 5D bounce model it can be seen that the evolution of equation of state(EOS)for dark energy ωde can cross over-1 at about z=0.23 and the current value ω0de=1.15＜-1.On the other hand,by giving a concrete expression of model-independent EOS of dark energy ωde,in the 5D bounce model we obtain the best fitting values zT=0.66+0311-0.08 and q0=-0.69+0.10-0.10(1σ)from the recently observed data:the 192 ESSENCE SNe Ia,the observational H(z)data,the 3-year Wilkinson Microwave Anisotropy Probe(WMAP),the Sloan Digital Sky Survey(SDSS)baryon acoustic peak and the x-ray gas mass fraction in clusters.