So couple of parts to this answer:
From version 5 the 2013 upgrade would be recommended, there are documents pages long on the improvements and fixes in the new version, it is better integrated with SQL, Office, 64bit service, etc...
The seamlessly bit depends on how customized your current system is, each customization needs to be reviewed and a call made
- Is it still required
- Can it be done in standard now
The developments that pass the test need to be transferred into the new system
The other big part will be the reporting, the reporting aspects have been redone in NAV 2009 RTC and up so that you may end up having to redo some of your custom reports, however you now are able to directly PDF and send to Excel from the reporting client so there is real benefit
The conversion to the cloud will depend on your business requirement, local servers will almost always be faster than cloud servers, but there is a backup, redundancy & maintenance benefit to having the server sit with people who specialize in servers, also if your business is distributed across multiple sites having it it the cloud will give a lot of benefit as the hosting provider will have better bandwidth
I haven't run NAV with office 365 yet, but can confirm that NAV 2013 runs fine with Office 2010 as that is what our clients all currently use
Hope this helps
Nev