Is there any budget lens for Nikon d5600 which is best for both portrait and landscape? I'm looking for one lens which does both portrait and landscape.
The most important part of taking good portraits is not the lens. It is capturing interesting subjects in good light. The percentage of good portraits will go up more quickly by improving lighting technique (and perhaps equipment) than by improving lenses. These days, many good portraits often entail post processing. Software and hardware and knowledge relevant for post processing may also significantly improve the quality of portraits. Having an appropriate wardrobe and finding good locations will also have a bigger impact on portrait photographs than the lens. So will a tripod (and perhaps a used Mamiya RB67 set upon it).
Similarly with landscapes. Interesting subjects in interesting light will have more impact than a particular lens. Techniques involving long exposures and post-processing multiple exposures and neutral density filters will also have more impact on the quality of a landscape image than a particular lens. And if the goal is pursuit of Ansel Adams level, it's film and a view camera with movements.
In the end, effort and applied knowledge have more influence on photographic results than the quality of equipment. Shopping for better equipment is easier than learning to take better photographs. Learning to take better photographs means understanding the compromises that are inherent in every piece of photographic equipment.
Reading the comments, I feel you "do not get the picture".
budget lens for Nikon d5600 which is best for both portrait and landscape
The best lens that covers that is... the Kit lens. That is why they provide it. Budget+Best+Portrait+Landscape. I must say, these lenses are quite good, not only for the price but for the overall result.
If you really learn how to use it you will get good images.
If you are not satisfied with the results there is a chance a lot of things are somehow wrong. Light, exposure, composition.
Beyond that you need either an EXPENSIVE lens that can do both (basically a wider aperture+sharper zoom lens)
or one economic 50mm f/1.8 lens to do portraits and use the kit lens for the landscapes.
If you are a student, and you are learning photography, i sugest you learn about this, and do not expect any magical solutions. n_n
One option is that you find an used lens with an aperture of at least 2.8. Take a look at this table: https://www.nikonusa.com/en/nikon-products/camera-lenses/all-lenses/index.page
And filter the options.