5 - 5.5 are normal blood sugar levels, it always rises after a meal but the vital thing is not to stress cells by having blood so high in sugar that water is drawn out of cells suddenly, to dilute the blood again (osmosis). Slow rise to 10 is okay after a meal.
The main problem is with starch and sugary drinks which provide immediate glucose sugar for absorption and the concentration rises in the blood too quickly. Thus sugar (sweets, etc.) and flour (pasta, rice, bread, cakes, biscuit, etc.) are difficult as the fat cells in diabetics don't take in sugar fast enough to keep the blood sugar level balanced. (This uptake is triggered by insulin, hence the connection.)
So, diabetics can eat as much fruit (no fruit has problem levels of sugar, except bananas with starch) and vegetables (except potatoes with starch) as they want and can fill up on them. Protein in meat, fish, eggs & cheese) take a long time to digest so the sugar (what little there is,) is not available quickly enough to cause stress in the cells. Similarly fats, so full cream milk, cheese & yogurt are fine and provide the vitamins A & D, & calcium for bones (vital to minimise osteoporosis) that margarines do not have. Proteins & fats do not cause sudden increase in blood sugar and can be eaten freely.
The only caveat is that if too much is consumed then bodies store it, weight increases and fat cells get more reluctant to take in the excess sugars - hence diabetic problems.
I hope this helps. My DH and DD are diabetic, so as a biologist, I have explored the subject.
Please beware of 'diets' - almost all advertised ones - and the easy damnation of fats in general.