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See Trac 2516 for the present status of "symbolic" hypergeometric functions. However, as DSM is alluding, we have a number of ways to get them.

Mpmath:

sage: import mpmath
sage: mpmath.hyp2f1(2,3,4,5)
mpc(real='0.15654212933375475', imag='0.15079644737231007')

Maxima:

sage: maxima.hgfred([2,3],[4],5)
3*(8*(log(-4)/25-1/20)+16*(13/400-2*log(-4)/125))/4
sage: maxima.hgfred([2,3],[4],5).n()
0.156542129333755 + 0.150796447372310*I

Probably other parts of Sage as well.