If you want to use Debian packages (corresponding to the ARM toolchain), you should install gcc-arm-none-eabi which provides C and C++ cross-compilers for 32-bit ARM, including Cortex-R processors:

apt-get install -y --no-install-recommends gcc-arm-none-eabi

The compiler command for C++ will then be arm-none-eabi-g++.

If you need the STL, you should also install libstdc++-arm-none-eabi-newlib:

apt-get install -y --no-install-recommends libstdc++-arm-none-eabi-newlib

armr5-none-eabi-g++ is (was) available in the Xilinx SDK; the relevant SDK nowadays would appear to be Vitis. For a container image you’d probably be best off installing it using the full unified installer archive. (I haven’t tried this so I can’t confirm that the armr5-none-eabi is included in current versions.)

C++ requires that the math functions be part of the basic runtime while C allows them to be in a library. The GCC implementation achieved this by automatically linking libm in a C++ build.

There are many other differences in the link phase; C++ linking will consistently fail if a C linker is used.

For a C link, use the C linker and specify -lm to make libm available.

On Debian and derivatives, the package you’re looking for is gcc-arm-none-eabi:

apt install gcc-arm-none-eabi

To find this out yourself in future, install apt-file, update your indexes and use it to search for commands:

apt install apt-file
apt-file update
apt-file search bin/arm-none-eabi-gcc

Here is an excellent doc.

Tool chains have a loose name convention like arch [-vendor] [-os] - eabi

 arch -    refers to target architecture (which in our case is ARM)
 vendor -  refers to toolchain supplier
 os -      refers to the target operating system
 eabi -    refers to Embedded Application Binary Interface

some illustrations as follows :

• arm-none-eabi - This tool chain targets for ARM architecture, has no vendor, does not target an operating system and complies with the ARM EABI.
• arm-none-linux-gnueabi - This toolchain targets the ARM architecture, has no vendor, creates binaries that run on the Linux operating system, and uses the GNU EABI. It is used to target ARM-based Linux systems.