Since any single connection on your network can carry up to 100 Mbit/s, the most used connection -- usually between the switch and the local server, proxy, router, or upstream switch -- will be the bottleneck. If you have ten computers all using the same connection, even for a small part of the way, they will share the 100 Mbit/s bandwidth.
In theory, if your computers communicate paired, each computer should be able to send and receive 100 Mbit/s (at the same time if using full duplex). The amount of data flowing over the switch would be 200 Mbit/s × the number of computers. (For a 10/100/1000 switch, substitute 1000 Mbit/s and 2000 Mbit/s, respectively.)
In practice, switches are limited either by a maximum bandwidth, or by the total number of packets it can transmit per second, whichever is reached first. One example of this is that when using small packets, you can achieve only a small fraction of the theoretical bandwidth -- although most of that is because sending millions of packets per second is a huge task for a CPU and an operating system.
Most small (up to eight ports) switches use common dedicated chips to do this, and typically should be able to reach near theoretical bandwidth limits with fairly small packets. Switches that have more ports, need comparably faster backplanes, higher bandwidth limits and packets per second. For rack-mounted switches, the manufacturers seems to document the switch limits pretty accurately, but you may need to read the manuals very carefully to parse them; the wording may be convoluted. (Pay attention to the packet size used for bandwidth or packets-per-second limits. Sometimes the size is unrealistic, so the values cannot be directly compared across manufacturers.)
In summary, just changing the switch will probably not help. However, if you change both the switch, and the NICs on the most used connection(s) -- to the server, or proxy, or upstream --, you likely will
see an improvement. This obviously depends on your network topology and traffic patterns, so there is no guarantee of an improvement.
In an office-like environment with up to a dozen or two computers, I'd much prefer GbE (1000 Mbit/s) NICs and switches and Cat6
cables -- Cat6a, if the price difference is less than 10%. While Cat5 is usually OK for GbE, Cat6 has much better shielding, and should be compatible with 10GBase-T, if affordable 10GbE NICs become available at some point. In electrically noisy environments, for example with power tools or large transformers nearby, I prefer shielded cables: FTP, FFTP, S-FTP, or STP (as opposed to normal UTP). If you can see a lot of packet errors, you might benefit from shielded cables; if you have none or just few packet errors, there is no need for the extra shielding.
Hope this helps.