That Gateway NV55S28u is certainly adequate for the type of workload that you mentioned.
And at $400 is a good value for a 1st notebook.
It's not especially strong at running modern games but does well running older titles and will run some less demanding recent games OK.
This AMD Radeon HD 6520G Review
should give you an idea how well it will run games.
For schoolwork / home entertainment it should get the work done over the next five years.
If there is a need to run more demanding games at higher graphics settings - that will be the area where it might not remain suitable over the next 5 years.