As far as scanning local Police for the Middlesex County area, depending on where you are, you would be out of luck as most are now digitally encrypted/scrambled. Only Woodbridge, Jamesburg/Helmetta, Milltown, South Brunswick, and County Sheriff are currently in the clear. Everyone else in Middlesex County as far as law enforcement are scrambled. I'm not sure about Dunellen Police, as they are on the Somerset County system, which I am out of range for monitoring. You would also need a P25 digital trunking scanner that can handle P25 Phase 2 digital mode communications with simulcast enabled. The only reliable scanners that can do this are the Uniden SDS series scanners, and Unication G4/5 (type) pagers. Everything else besides an actual public safety radio will get you less than desirable results and you'll become very frustrated with scanning. And if you do decide to purchase said scanners/pagers listed above, then expect to spend in the area of $500-$700, depending on what features and digital modes are installed in the radio already. Plus you would also need to properly program it, which is a learning curve. I'm from the Edison area, so if you have any further questions, you can respond to this thread or send me a private message.
As far as your Baofeng UV5-R radio, that's for the most part useless for scanning police frequencies for Middlesex County. It's an analog only radio, and you would only be able to scan the County Hotline and SPEN 1 (State Police Emergency Network) on it, which limits what you can hear.