On balance, for babies in developed countries, weaning at 4mo is probably very slightly optimal--but only assuming you are giving iron-rich foods and allergens.
The WHO advice is skewed towards the needs of developing countries, where you kind of want to delay weaning till the absolute last minute because giving anything other than breastmilk greatly increases the risk of gastro intestinal diseases caused by poor hygiene, and more breastfeeding by mothers acts as the best pregnancy spacer in environments where proper birth control is not available. The WHO acknowledges that iron deficiency is somewhat commoner when you delay weaning to 6mo, but has decided that the above two things are more important, on balance, in poor countries. And allergy prevention is not an issue in developing countries as babies are exposed to so many bugs in their environment anyway.
Of course, GI diseases caused by poor hygiene and the need to space pregnancies through more BFing are not terribly relevant to those of us in developed countries, so arguably the prevention of iron deficiency should take priority. And of course anything that makes allergies less common is a boon for us in rich countries because this is such an issue in our societies.
I gave small amounts of food starting from 4mo, based on the above. Including meat, iron fortified cereal, and all the allergens one by one. Will be doing the same with my current baby as it worked well last time and my older child is the only one among her cousins with zero allergies.
I did not give custard, however, and definitely not at 5 weeks! The OP's husband needs to understand that you don't just bung random foods into teeny babies for fun--that is just silly and potentially harmful.
That said, the differences involved either way are SMALL--it's not "bad" to wait till 6mo either. 4-6mo depending on parenting style and how you feel about solid foods is probably the best advice for the moment, until more robust evidence in either direction emerges.
scienceofmom.com/2015/05/14/starting-solids-4-months-6-months-or-somewhere-in-between/
Good read here.