you definitely need to change your psu, as 6670 requires 5 times more power on full load compared to 6450.
component max power consumption
6670 125w
6450 25w
i5 140-150w
so as you can see i5+6670=275 watt of true power consumption at their max load, note that hard disk drive, cd drive , ram, extra cooling fans are not included in power.
so conclusion is that upgrade your power supply around 400watt of true power