Few things need clearing up here. Firstly, 5kg dumbbells aint gonna do anything, unless you're currently so weak that you can only just squeeze out about 10 reps with them, and even if so you'll outgrow them mega quickly. If you're training biceps you need to train biceps too.
Secondly, I think you're expecting results way too quickly. You will indeed make significant gains in your first 6 months IF you do everything right, but if you're having protein shakes daily then you're not gonna be big by the time you finish a medium sized tub. Far from.
Lastly, PLEASE don't take the "eat all you can" approach as recommended above. When you're new especially, you'll either a) underestimate how much you're eating as many do, or b) unnecessarily get fat - you can only gain so much muscle per month, adding a bunch of fat in the process won't force any more growth. In your first year you only need a very small caloric surplus, or even eat at maintenance, to grow. My arms grew several inches without me gaining any fat in my first 6 months because I kept the calories sensible. ALWAYS count calories so you know you're eating enough/not too much - if you start getting noticeably fatter then you're overdoing it on the kcals, if the scales aren't going up as the weeks goby then add in a few hundred more calories. At your weight, maybe start at 2500 calories per day (I was pretty much the same weight as you when I started and 2500 to start with worked well for me) and get about 100-150g of protein per day. Doesn't matter where the rest of your calories come from in terms of results, IME.
Using a dumbbell only routine is absolutely fine if you get an adjustable set with more weights, but I'd also get a pullup bar and a foldable bench that you can tuck away whennot on use, a bob basic one for starters will cost you about 30 quid from Argos.I made significant progress starting on a dumbbell only routine with a bench and pullup bar too, full body workout 2-3x per week.