You can have a baby on a feeding schedule just as well if you are breast feeding. Breast feeding is ultimately THE BEST for your baby. It has soo many benefits such as helping babies fight sicknesses & it even makes it easier for babies to transition into solids because breastmilk somewhat takes the taste of whatever you eat so babies get used to different flavors...at least that's what i've read in several places. I have an 8mth old daughter & am also a 1st time mother. I had no problems getting my baby on a schedule. Of course when they are newborns or in your case only 5 weeks, they will be waking up at night, but that usually only lasts for the first 2-3 months. You can get all the info you need from a great website that La Leche League has. Just do a Google search for it (I don't remember the exact site). They have plenty of resources & information that you can show your husbnad from thousands of mothers! Also, there are MANY other resources on the web for the benefits of Breastfeeding.
Formula is fine for those who prefer it or cannot breastfeed but any doctor will tell you that breastfeeding is ultimately the best...if you think about it, Formula says it all in its name, its a formula created usually from cows milk & other substances that simulate breastmilk, so its not really as natural. In my opinion, the more natural, the better & as long is your baby is healthy & your pediatrician also gives your baby a clean bill of health, you are doing fine! You can get lots of info from your pediatrician too...maybe take your husband with you to the next baby appointment so he can hear it from them that you are doing just fine & that the baby is perfectly healthy.
Also, if you are planning to go back to work, you may want to start pumping your milk & freezing it, you can find out all the details on how long to freeze & the do's & don'ts on La Leche League website. I'm not sure how long you are planning to breastfeed but at least consider doing it for the first 3 to 6 mths. I personally am aiming towards a year for my baby.
Good luck & congratulations on your baby! Motherhood is great isn't it!