Answer
$P(I~win)=\frac{1}{324,632}=0.00000308$
Work Step by Step
The sample space: all the combinations of 35 distinct mumbers (from 1 to 35) taken 5 at a time:
$N(S)=$ $_{35}C_5=\frac{35!}{5!(30-5)!}=\frac{35!}{5!\times30!}$
But, $35!=35\times34\times33\times32\times31\times(30\times29\times28\times...\times3\times2\times1)=35\times34\times33\times32\times31\times30!$
$_{35}C_5=\frac{35\times34\times33\times32\times31\times30!}{5!\times30!}=\frac{35\times34\times33\times32\times31}{5\times4\times3\times2\times1}=\frac{38955840}{120}=324,632$
With one ticket: $N(I~win)=1$
Using the Classical Method (page 259):
$P(I~win)=\frac{N(I~win)}{N(S)}=\frac{1}{324,632}=0.00000308$