How to implement a lowpass filter for this one zero, one pole transfer function?
The best is to rewrite your transfer function in the proper low-entropy way, with a leading term. I have assumed the roots are all negative leading to left-half-plane pole and zero:

\$G(s)=\frac{s+5447}{s+961.3}=G_0\frac{1+\frac{s}{\omega_z}}{1+\frac{s}{\omega_p}}\$ where:

\$G_0=\frac{5447}{961.3}=5.66\$

\$\omega_z=5447\$ rd/s or 867 Hz

\$\omega_p=961.3\$ rd/s or 153 Hz

There are plenty of ways to implement such a filter. One way is to use an op-amp in an inverting configuration and have it followed by another inverting structure with a gain of -1:



You then calculate the values of the various components according to the below Mathcad sheet. These values can be determined using fast analytical techniques or FACTs.