Not losing weight while eating a ketogenic diet is very often attributable to eating far too much fat. It's extremely energy dense and you don't need to eat a lot to be eating too much. For example, just 100g of coconut oil is ~900 Kcal. Straight away that's ~900 Kcal that won't need to be oxidised from the body's own storage. Purely from a fuel perspective, you could survive on 200g of coconut oil, so it's easy to see how the fat can be overdone. If you have weight to lose, it's better to burn what you already have instead of putting more in. Swilling down kilos of dietary fat is possibly the most common keto mistake. Too much protein can also be a factor for some, particularly if they're super insulin resistant.
With regards to the glucose, it's not uncommon for fasting numbers to rise in the earlier stages of ketogenic eating. The lower circulating insulin is allowing glucose to come pouring out of every nook and cranny instead of staying locked up in tissues and organs. This is good - it means you can burn it off. Initially, I would be paying more attention to overall trends, as fasting numbers are almost always the very last to fall off a cliff.
Or of course it may also be that you're simply not suited to keto, but it would be highly unusual to not lose any weight and not see any glucose regulation benefits at all. Also, for reference, it took me the better part of an entire year of hardcore keto in order to regain tip-top glucose control (I had no weight to lose). Five weeks is nothing in the grand scheme. Some see huge improvements in that timeframe, and some don't.
Best of luck with everything.