I think it is a healthcare cost risk call. $5k deductible risk vs ability to make a $3,350 HSA contribution.
Now cost to you of the $3,350 contribution may be just $2,093.75 using 25% federal tax rate, 5% state tax rate, and 7.5% fica tax rate (Herring mentioned this below so definitely use payroll deduction if at all possible).
If about $2,093 to get $3,350 into an HSA is worth the risk of up $5,000 in possible healthcare costs is a good bet, go for it.
I think this is on the money.
Situations where the employer pays all or almost all of the premium really distort the HDHP+HSA versus traditional insurance question. If the insured person pays most of the premium, HDHP with HSA usually wins because of the tax advantage of the HSA and the opportunity to keep your money if you don't consume healthcare services. But in your situation you could very well find that pursuing the tax benefit is potentially detrimental to your overall financial well being. Don't let the tax tail wag the dog that is your overall financial condition. Taxes are only one piece of your finances.
You say the deductible on the other plan is "negligible" but that doesn't really help with the comparison. Does negligible mean $500? $1000? What is the coinsurance percentage after you hit deductible? What are the copay costs?
The way I would analyze your situation is to analyze it with the assumption that you hit your out of pocket maximum. How much are you on the hook for in that instance? How much in medical bills would you have to accrue to reach the out of pocket maximum?
If you take the HDHP/HSA, you get $1250 in tax savings by taking on $5000 of risk with no additional premium savings. One year hitting the OOPM would wipe out four years of tax benefits. If you go the traditional plan route, your maximum out of pocket exposure will be significantly less and you will get financial assistance with the medical bills sooner in the form of copays or coinsurance at no additional premium cost.
My guess is that you would be better off with the traditional plan. If your out of pocket costs are truly negligible, it makes no sense to take on the extra financial risk of the HDHP. If so, be thankful that you work for an employer that provides a low-deductible plan at no cost to you and forget about the HSA's tax benefits.
Does your employer offer a flex spending account where you could set aside some tax-free use-it-or-lose-it money to pay for medical bills under the traditional plan? This may be a way to get the best balance of tax advantages and limited potential liability.