Can my landlord make me pay a whole months rent for only being here for 5 more days?

If it qualifies, you may have the right to terminate the lease without or with a smaller penalty due to the deployment of your husband.

Under Section 535 of the Service Member Civil Relief Act, a military member has the right to terminate a lease, if, after signing the lease: the tenant enters military service (which includes a reservist being called to active duty); or the tenant signs the lease while in military service, and then receives military orders for a PCS move, or to deploy, or as an individual in support of a military operation, with a military unit for a period of not less than 90 days.

Your landlord can absolutely do that. If you have a lease with your landlord, two things can happen. Either your landlord will allow you to surrender your lease without any penalty and give most of your security deposit back minus any repair or cleaning fees. Or, the more likely event is you are responsible for the rent owed for the rest of your lease even if you don't live there. Your landlord is not off the hook and must mitigate his damages by working on obtaining a new tenant. Once that occurs, then you are off the hook. That is why most landlords will simply begin deducting rent owed from your security until more is needed because the security has been exhausted.