WDS bridging is a feature in a few different routers stock firmware. In general it works best when the two bridged routers are of the same model. I don't recall if the WRT54GL has this feature in its stock firmware or not.
Client mode is an even rarer feature in stock firmware, and few routers have this capability unless you can and do use something like dd-wrt 3rd party firmware on those models. I don't know if the stock WRT54GL supports this mode.
The manual you download from linksys for the model should say if its stock firmware supports WDS bridging mode and/or client mode.
I meant that the WRT54G-L model has bigger flash ROM, more RAM, and is designed to be easily (relatively) able to be flashed to the full featured version of DD_WRT and similar 3rd party firmware. When you convert this (L) model of router it should be possible (IIRC) to do it with a few less steps / complications than converting the firmware in the V5 WRT54G model you said you had. And in the end the (L) model's greater flash / RAM capabilities will let you run somewhat more sophisticated / capable firmware on the (L) unit. I suspect, though, that even the V5 will do what you need once you do get it updated to DD_WRT. Check their site for limitations / features of the edition compatible with the V5 or whatever you have.
If you want an out-of-the-box client mode or wds bridge mode solution you'd be looking at replacing both of your routers, though at the moment I don't know what routers to recommend that have those features in stock firmware. I know several do have it though. It may be possible to buy a pre-flashed DD-WRT router from someone too, but I don't know the details of that.
Doing the TFTP and VX works killer program shouldn't be all that bad, though, for your current V5.. maybe 1 hour of fooling around and studying the steps required. The worst that'll happen is that you'll break the router and have to get a new one anyway (aside from some wasted effort/time). I'd try it if the site suggests that it is compatible / possible / useful.