Another laptop? So quick question how does your current laptop perform?
Simple answer yes
Complex answer depends
Without going into major details about compression, codec's, bitrates etc. are only wanting to view streamed content? If so it really depends mainly on bandwidth and the platform streaming the data (and the quality of said data) rather than the overall power of your computer. (Software/ codecs not withstanding).
Example I have only 8meg down but I can view 1080 video fine if I wait a little while for the video to partially buffer however a 720 will be fine to watch without buffering – depending on the platform:
YouTube for me – 720 yep fine 1080 it freaks out (due to the way it buffers).
Vimeo – any resolution fine but the higher (typically anything over 720) needs time to buffer, the higher the resolution the longer the time.
As with downloading a file, size and compression reflects how long it will take depending on bandwidth available.
you mentioned streaming as well as YouTube videos – do you want to stream or create content yourself? If so that has other considerations as well as similar ones.
However *buying a new laptop/ computer standard response*
I always say buy the most powerful laptop/ computer for your budget, it will 'last' longer and be more flexible so you use it for more powerful applications but if you want something only for a specific task you can budget down so to speak.
Mind you, you didn't specify which Pentium processor the laptop came with