Inspiron 5675, new power supply?

Your Inspiron 5675 supports standard ATX power supply (with 24-pin power connector on motherboard).  OEM systems shipped with 300w, 460w or 850w PSU, you can search your local markets (online or computer stores) for a suitable PSU of your budget and your needs.  See system specs.

Take precaution when working on your system.  Here is the service manual and the process of removing the power supply unit.

Select compact design with a depth of 140mm for a perfect fit drop-in replacement.  Example of power supply on big shopping site. 

@Chino de Oro​ Thank you for your help. Was just wondering if there's anyway to ensure the plug is the correct size?

Dell computer power cables for US customers are standardized based on whether you are connecting to a wall outlet or a data center power distribution unit (PDU). Standard laptop and desktop cables feature a NEMA 5-15P (3-prong US wall plug) to an IEC 60320-C13 (device connector), rated for 125V at 10A to 15A

UK Dell PC power cables (mains leads) feature a standard 3-pin UK plug (Type G / BS 1363) with a 5A or 10A fuse on one end, and an IEC-320 connector on the other. Standard Dell desktop PCs and monitors use a C13 "kettle" lead, while smaller Dell devices may use a C5 or C7 connector

Dell uses switching power supplies that accepting input voltage from 100V to 240V AC.  Although the receptacle is different according to regions, the connector at power supply is generally has the same fitment.  

Therefore, you can reuse the external power cable (the standard cord that plugs from the wall into the back of your PC).  However, most if not all of the retail power supplies on the market will provide you a new power cord that would be compatible with your computer and region power outlet.

Below are Dell part numbers for the Inspiron 5675 850W PSU you may use in searching on the web =

48Y6D 850W Huntkey
N1WJD 850W Delta

If OP’s 5675 has a slim dvd, traditional standard ATX psu may not supply a slim sata power connector for the slim dvd. Traditional atx psu still supply lots of 15 pin sata and 4 pin molex connectors from bygone years with intention of supplying everything any builder would need (whether it is a modern build or retro build), which may be excessive in the era of m.2 ssd.