Aspire V5, with AMD c-70 processor and 4 GB ram can run minecraft well. It has the maximum storage capacity that is required and it is also a 64 bit system. You should make sure that it has a Java SE 6 Update 32, Java SE 7 Update 4 or a higher version.
Is it a single core, dual core, quad core cause that makes a big difference. If you have a dual or a quad then yes it should run it very well as long as you don't have too much programs to take CPU or VIRUSES!