Does my spouse have to file his taxes if he grossed less than 5,000.00 last year?

It depends on your filing status. If you are planning to file as Married Filing Jointly then you do not have to file if your combined gross income is less than $18.700. But if you are filing as Married Filing Separately then yes - he must file a retiurn since his gross income is greater than $3,650. For details, look at Table C on page 8 of the instructions for Form 1040:
http://www.irs.gov/pub/irs-pdf/i1040.pdf

One other thing - even though he may not be required to file, it may be advantageous to do so - for example to get back any withholding that may have been taken from his wages, or to qualify for credits such as the Earned Income Credit.