  We report the discovery of ten new pulsars in the globular cluster Terzan 5
as part of the Transients and Pulsars with MeerKAT (TRAPUM) Large Survey
Project. We observed Terzan 5 at L-band (856--1712 MHz) with the MeerKAT radio
telescope for four hours on two epochs, and performed acceleration searches of
45 out of 288 tied-array beams covering the core of the cluster. We obtained
phase-connected timing solutions for nine discoveries, covering nearly two
decades of archival observations from the Green Bank Telescope for all but one.
Highlights include PSR J1748$-$2446ao which is an eccentric ($e = 0.32$)
wide-orbit (orbital period $P_{\rm b} = 57.55$ d) system. We were able to
measure the rate of advance of periastron ($\dot{\omega}$) for this system
allowing us to determine a total mass of $3.17 \pm \, 0.02\, \rm M_{\odot}$.
With a minimum companion mass ($M_{\rm c}$) of $\sim 0.8\, \rm M_{\odot}$, PSR
J1748$-$2446ao is a candidate double neutron star (DNS) system. If confirmed to
be a DNS, it would be the fastest spinning pulsar ($P = 2.27$ ms) and the
longest orbital period measured for any known DNS system. PSR J1748$-$2446ap
has the second highest eccentricity for any recycled pulsar ($e \sim 0.905$)
and for this system we can measure the total mass ($1.997 \pm 0.006\, \rm
M_{\odot}$) and also estimate the individual pulsar and companion masses. PSR
J1748$-$2446ar is an eclipsing redback (minimum $M_{\rm c} \sim 0.34\, \rm
M_{\odot}$) system whose properties confirm it to be the counterpart to a
previously published source identified in radio and X-ray imaging. With these
discoveries, the total number of confirmed pulsars in Terzan 5 is 49, the
highest for any globular cluster so far. These discoveries further enhance the
rich set of pulsars known in Terzan 5 and provide scope for a deeper
understanding of binary stellar evolution, cluster dynamics and ensemble
population studies.
