I know its basic and simple but I want to make sure I've got the equation correct. Here's the query...

There are 100 tickets available for a raffle. If I buy one ticket, my odds are 1 in 100. If I buy 5 tickets do my odds become 1 in 20?

Just need one of you math whiz guys to correct me if I am screwing that up.

Just to be clear, you are assuming:
- only one prize
- prize winning ticket is randomly chosen with each ticket having the same chance of being chosen
- all 100 tickets are sold

Then, clearly, if you buy one ticket the probability of you winning the prize is 1/100.

And if you buy 5 tickets the probability of you winning the prize is 5/100 (or 1/20).

Are you asking about the semantics of "odds" (the relationship between odds and probabilities)?

Yes.

If you want confidence in your calcs then it's always good to come to the same result using two different approaches. One you already have. The other is this way:

In probabilty it's almost always better to think about the question from the other side. i.e.:

"What are my chances to win within 5 draws"
becomes
"What are my chances not to lose with 5 draws"

The other consideration is: All probabilities for all possible outcomes always have to add up to 1. So
"chance to win within 5 draws" + "chance to lose with 5 draws" = 1
or
"chance to win within 5 draws" = 1 - "chance to lose with 5 draws"

So all we have to figure out is what the probability for "chance to lose with 5 draws" is.
Chance to lose on draw 1: 99/100
Chance to lose on draw 2: 98/99 (since one ticket is now already gone we have to divide by 99 not 100)
Chance to lose on draw 3: 97/98
etc.

Plug that into the equation and it looks like this:
"chance to win within 5 draws" = 1 - (99/100 * 98/99 * 97/98 * 96/97 * 95/96)

Plug into calculator and you get
"chance to win within 5 draws" = 5%