As others have suggested you need to have a sit-down with your boss -- Schedule an off-site "long lunch meeting" or a full afternoon with no distractions and come prepared: You have been at this company for 5 months, you know what's broken and (hopefully) have some long-time ideas on how to fix it.
Once you and your boss are somewhere quiet you need to discuss the expectations of the company, the problems you are aware of, any problems you may not be aware of (the "political landscape" between your company and your clients), and the reasons you can't currently meet expectations (technical, procedural, staffing, "unreasonable expectations", etc. -- Note that by "unreasonable expectations" I mean things like "and we want zero downtime EVER!", not stuff that could be solved by more hardware, better management practices, more bodies and the like).
Having discussed the situation present your boss with your plans to improve things, rough estimates of capital and manpower costs. It's best to have at least 3 options (Lousy solution, the solution you'll probably implement, and a Cadillac solution that's bomb-proof and mostly future-proof) with good reasons backing them up, and to have roughly 3-month timetables for hitting milestones.
If your boss and company don't suck you'll get buy-in to make things better (and help overcoming any client resistance to change/downtime), and your job will start sucking a whole lot less.
Having written all that, note that sometimes a company just won't be ready to take the plunge and invest in the amount of work required to make a sysadmin's life not suck, or they may not have the political capital with their clients to push changes upon them.
Bitter Experience has taught me that if your management isn't willing to work to implement sound plans to make the environment better it's often a good idea to pack your bags and move on.
If it comes down to it, give your notice (at least 2 weeks), provide them as much documentation as you can on the current state of the environment during your notice period (this will be invaluable to your successor and may help them get changes made), and leave on terms that are as cordial as possible. Resume-wise, indicate your accomplishments and the technologies you worked with/responsibilities you had, and be prepared to explain in an interview the problems you encountered, the solutions you proposed, and that you left because the environment was unworkable and the company was unwilling to work with you to improve it.
You can/should describe problems/proposed solutions generically, and obviously don't slander your previous employer (makes you look bad), but don't be afraid to say "I left because the environment was a disaster, they wouldn't work with me to fix it, and I can't spend 24 hours a day 365 days a year putting out fires." In nicer terms of course.