Converting Coordinates formatted as Lat 4531.38153 Long 12347.2328 to Decimal Degrees?

They look like Degrees Decimal Minutes (DDM) with the degree and minutes symbols dropped.

Try reading Lat 4531.38153 Long 12347.2328 as Lat 45° 31.38153' Long 123° 47.2328'

You may find this PGC Coordinate Converter useful.

I suppose it might be NMEA. It has quite strange coordinates representation: lat is DDMM.MMMMM and lon is DDDMM.MMMMM.