The length of your marriage has little to do with the amount of alimony, or spousal support, to which you may be entitled. Rather, it has much more to do with the length of time you may receive support.
A 5-year marriage is definitely long enough for a spouse to receive support. Under Family Code Section 4320, the presumption is that you should receive support for approximately half the length of the marriage if the marriage is less than 10 years long.
It's called spousal support, not alimony, and yes, a 5 year marriage isn't a presumptive 10 year "long term" marriage, but you should be able to get some support. The family law judge will look at your and your husband's respective educations, earnings in the past, capacity for future earnings, assets, expenses, etc.
If he's the one with the money, your dissolution papers can also ask the judge to order him to pay your legal fees as well as his own.
See a family lawyer for help.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.