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

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.

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.

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.