The better move is 1. H3+4. Actually, it's very difficult
to profoundly analyse this complicated position. I'll give
only a few lines and hope that there won't be too many
protests. Of cause, we could try to go more into detail
with a discussion in the forum section.
1. C5+3? as seen in the actual game is premature and allows
Black to activate his pieces and launch a promising counter attack.
1.C5+3? H7+8! 2.R1.4 R9.7 3.C5+1 (3.H3-1 C2+6 4.A6+5 H+-6 or
3.H3-2? H-+6 are worse) 3. ... R7+6 4.R6.2 R7-1 5.H8+7 R1.4
6.C6+3 R4+3 7.C5-1 R4+1 (Answer 1) and Black has
a lot of active plans like C2+2 or C8.7 or H8+7. In the actual
game Red played 8.E7+5 R7+2 9.R4+4? (9.K5+1 is necessary but
Red has many problems after 9.K5+1 R7.6 10.K5.4 H8-6) 9. ... R4.5.
Black's pieces are much more active.
Red could have avoided that by playing 1.H3+4, he can take Black's
central pawn later. Again, the game is far from being over but
now Red has better chances to develop an initiative. See some
A) 1.H3+4 H7+8 2.H4-2 C8+4 3.C5+3 C8.1 4.C6.9 R1.4
5.R6+4 K5.4 6.R1.6 C2.4 7.R6+5 (Answer 2) threatening 8.C9.6
B) 1.H3+4 H8+7 2.C5+3 C8.7 3.C6+2 R9.6 4.C6.3 R6+4 5.C3+4 C2.7
6.E7+5 R1.2 7.H8+7 (Answer 3)