The system is has solutions.
You can use Singular, which is part of Sage:
http://www.singular.uni-kl.de/Manual/3-1-0/sing_1273.htm
> ring r=0,(x,y),lp;
> ideal i=x2+y2-25, x2-y2-y-5;
> LIB "solve.lib";
// ** loaded /sw/share/Singular/LIB/solve.lib (1.39,2009/04/15)
// ** loaded /sw/share/Singular/LIB/triang.lib (1.14,2009/04/14)
// ** loaded /sw/share/Singular/LIB/elim.lib (1.34,2009/05/05)
// ** loaded /sw/share/Singular/LIB/ring.lib (1.34,2009/04/15)
// ** loaded /sw/share/Singular/LIB/primdec.lib (1.147,2009/04/15)
// ** loaded /sw/share/Singular/LIB/absfact.lib (1.7,2008/07/16)
// ** loaded /sw/share/Singular/LIB/matrix.lib (1.48,2009/04/10)
// ** loaded /sw/share/Singular/LIB/nctools.lib (1.54,2009/05/08)
// ** loaded /sw/share/Singular/LIB/random.lib (1.20,2009/04/15)
// ** loaded /sw/share/Singular/LIB/poly.lib (1.53,2009/04/15)
// ** loaded /sw/share/Singular/LIB/inout.lib (1.34,2009/04/15)
// ** loaded /sw/share/Singular/LIB/general.lib (1.62,2009/04/15)
> def R=lex_solve(std(i));
// 'lex_solve' created a ring, in which a list rlist of numbers (the
// complex solutions) is stored.
// To access the list of complex solutions, type (if the name R was
assigned
// to the return value):
setring R; rlist;
> setring R; rlist;
[1]:
[1]:
-3.645398168574155899469652036354
[2]:
-3.422144385112380095048443186522
[2]:
[1]:
3.645398168574155899469652036354
[2]:
-3.422144385112380095048443186522
[3]:
[1]:
-4.057224690913259002509197930026
[2]:
2.922144385112380095048443186522
[4]:
[1]:
4.057224690913259002509197930026
[2]:
2.922144385112380095048443186522
Michael
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