High throughput send to EventHubs resulting into MessagingException / TimeoutException / Server was unable to process the request errors

Send throughput tuning can be achieved using efficient partition distribution strategies. There isn't any single knob which can do this. Below is the basic information you will need to be able to design for High-Thruput Scenarios.

1) Lets start from the Namespace: Throughput Units(aka TUs) are configured at Namespace level. Pls. bear in mind, that, TUs configured is applied - aggregate of all EventHubs under that Namespace. If you have 5 TUs on your Namespace and 5 eventhubs under it - it will be divided among all 5 eventhubs.

2) Now lets look at EventHub level: If the EventHub is allocated with 5 TUs and it has 32 partitions - No single partition can use all 5 TUs. For ex. if you are trying to send 5TU of data to 1 partition and 'Zero' to all other 31 partitions - this is not possible. Maximum you should plan per Partition is 1 TU. In general, you will need to ensure that the data is distributed evenly across all partitions. EventHubs support 3 types of sends - which gives users different level of control on Partition distribution:

1. EventHubClient.Send(EventDataWithoutPartitionKey) -> if you are using this API to send - eventhub will take care of evenly distributing the data across all partitions. EventHubs service gateway will round-robin the data to all partitions. When a specific partition is down - the Gateways auto-detect and ensure Clients doesn't see any impact. This is the most recommended way to Send to EventHubs.
2. EventHubClient.Send(EventDataWithPartitionKey) -> if you are using this API to send to EventHubs - the partitionKey will determine the distribution of your data. PartitionKey is used to Hash the EventData to the appropriate partition (algo. to hash is Microsoft Proprietary and not Shared). Typically users who require correlation of a group of messages will use this variant of Send.
3. EventHubSender.Send(EventData) -> In this variant, the Sender is already attached to the Partition. So - this gives complete control of Distribution across partitions to the Client.

To measure your present distribution of Data - use EventHubClient.GetPartitionRuntimeInfo Api to estimate which Partition is overloaded. The difference b/w BeginSequenceNumber and LastEnqueuedSequenceNumber is supposed to give an estimate of that partitions load compared to others.

3) Last but not the least - you can tune performance (not Throughput) at send operation level - using the SendBatch API. 1 TU can buy a Max of 1000 msgs/sec or 1MBPS - you will be throttled with whichever limit hits first - this cannot be changed. If your messages are small - lets say 100 bytes and you can send only 1000 msgs/sec (as per the TU limit) - you will first hit the 1000 events/sec limit. However, overall using SendBatch API - you can batch lets say 10 of 100byte msgs and push at the same rate - 1000 msgs/sec with just 100 API calls and improve the end-to-end latency of the system (as it helps service also to persist messages efficiently). Remember, the only limitation here is the Max. Msg Size that can be sent - which is 256 kb (this limit will apply on your BatchSize if you use SendBatch API).

Given that background, in your case: - Having 32 partitions and 5 TUs - I would really double-check the Partition distribution strategy.

here's some more general reading on Event Hubs...