Your DH needs to stop listening to his DM and supporting you more!
. My DAunt kept telling me she gave my Dcousin “full dinners” at 6 weeks. She seems to ignore the fact that he’s got horrific asthma and had a heart attack at 27!
Get him to read What to expect in the early weeks.
WHO are also very, very clear on introducing solids and it’s not before 6 months. Have a look at their guidelines here. There was some controversial “research” published saying it’s fine from 4 months but the said research isnt really valid as it was funded by Nestle who have a vested interest in you stopping Bfing
.
There is also clear research that says introducing solids before 17 weeks is a serious allergy risk.
Get him to read the NHS Guidelines on starting solids as it gives the signs of readiness.
This is a good article too on Dads and breastfeeding.
As is the MN info on starting solids.
And Kellymom on starting solids.
Really though, Weaning isn’t something you need to be worrying about at 5 weeks, it’s ages away! 
Your DMIL had her babies a long time ago, she needs to realise that there’s been a hell of a lot of research since then and all of it is really clear on holding off offering supplemental foods until 6 months 
Congratulations on your new LO too 