From Förberedande kurs i matematik 1

The notation ln is used for the logarithm with the natural base \displaystyle e=\text{2}.\text{7182818}...,

and we therefore have that \displaystyle \text{ln }e=\text{1}, which together with the logarithm law, \displaystyle b\lg a=\lg a^{b}, gives that

\displaystyle \ln e^{3}+\ln e^{2}=3\centerdot \ln e+2\centerdot \ln e=3\centerdot 1+2\centerdot 1=5