@Sokolov To learn about resistance training I would recommend watching: Natural Hypertrophy, Eric Bugenhagen, Alex Leonidas, Basement Bodybuilding, and GVS. As you watch their videos and workout you will over time learn what best works for you and how to form training routines. Since, you only have 5kg DBs you will have to center everything around calisthenics, most importantly: pull ups, push ups, sit ups, and squats. These 4 exercises can be good enough for a long time if you keep making them progressively harder as you improve. If you have time and will don't limit yourself though, with DBs you can do a lot of typical "isolation" exercises so try and explore different exercises.
For calisthenics you'll need a pull up bar. Parallel dip bars could be also nice as they allow you to do body rows and not only dips which might be good stepping stone towards pull ups. A few resistance bands will be a good investment as well as you can attach them to doors or something and use them like cable machines.
Being skinny doesn't always imply good metabolism so unless you know better it's not given. Track calories for a few days to see how much you actually eat as likely you're under-eating. Then do simple maths to figure out how much you need to eat to gain weight (working out alone won't be enough).
Intense weightlifting is not "optimal" and peaty, so some might suggest doing eccentric only and generally take it easy to reduce stress, etc. but deviating from pure peatism and training intensely, IMO, will teach you more and you'll progress faster. Such "optimal" fancies rarely work from what I've seen and the traditional heavy lifting is more effective.
Hope it helps.