You can't use a mere R4 or R5 Radeon. The minimum AMD gaming card starts from the lowest of the R7s. Comparing Pre- "R-range" cards with their predecessors isn't simple, but the R4s and R5s are equivalent to HD 7350s and HD 7470s.
Battlefield 4 System Requirements
Minimum Requirements
INTEL CPU Core 2 Duo E6700 2.6 GHz
AMD CPU Athlon 64 X2 Dual Core 5800+
Graphics Card: AMD Radeon 3870 or higher; NVIDIA GeForce 8800 GT or higher
RAM 4 GB
OS Win 7 64
Direct X DX 10
HDD Space 30 GB
Laptops have their GPUs locked inside, so upgrading those isn't normally an option.
