Are 5 year combined BA engineering/MBA programs worth the extra time and expense?

Software engineering is mostly about experience. What you get at college can be a good base, however internships and personal projects are where you will get most of your practical experience to help navigate the waters of finding a career in software engineering.

It's really nice to have some actual work experience before your get your MBA. I think you can get more out of the program plus the network you develop is a nice plus so it's a great step for down the road when you have a better idea of what direction you want to go or reach a point where you feel you need a career change. Some employers will sponsor or help pay for at least some of the mba expenses. However, the cost of top tier MBAs is growing so high, it isn't a terrible thing if you can afford it and get it all done early on - at least you will have gone and done it and not have a 2 year break to contemplate and try to pay for or try to juggle on top of a full time job. Lots of pros and cons.

I've been in engineering/ engineering management in the chemical business for 35 years before retirement. Many plant managers and business sector leaders have an engineering degree and an MBA, but I would not be to too much of a hurry for the MBA. You could find the company that you like and perform as an engineer and then get a masters if you wanted to explore the business side. Many engineers I know have preferred to stay in a technical role rather than management or business. If business interests you, many major companies pay for the masters degree. God luck.