I would definately buy the New Dr Who seasons 1 to 4 boxed set (Doctor Who: Series 1 - 4 Collection [DVD]) first, as it's so cheap [for 23 DVDs] and it's all you need to know as it assumes no prior knowledge of the previous 20 odd Dr Who seasons that came before it. The first four New Dr Who seasons have some fantastic storylines [e.g. Bad Wolf] and follow the adventures of the previous ninth and tenth Doctor incarnations. The first 4 seasons also introduce all the doctor's enemies [and friends], and so by season 5 it is assumed you know all about them already.
I myself started with season 1 because I like Chris Eccleston. Next I bought The Christmas Specials to watch Tim Dalton. [Later I bought the seasons 1-4 box set because I became a fan of Doctor Who.] I was able to understand the stories then. So I think you can start watching season 5 without watching previous seasons.