Do you know if that crankset will work fine with the SRAM x5 parts which are currently on my bike?
I'm not sure if there would be any problems mixing SRAM and Shimano per se. The SLX crank is a higher end component than the X5, so you would be buying more than you need, and you get problems mixing 9 and 11 speed components.
The 11 speed SLX crank uses a narrower chain than 9 speed. The 11 speed chainrings are slightly closer together which may give you shifting problems and chain rub as your front derailleur is designed for 9 speed chainring spacing.
By choosing a 24/32 crankset instead of 22/36 you'll be loosing high and low ratios. The smaller chainring gap on the SLX is made up for by a wider spread of sprocket sizes available in 11 speed cassettes.
Upgrading one component several steps - even something major like the crankset - does not make a significant difference to the bike overall, and here you'd be introducing other problems. Better to play it safe and get a SRAM crank. I think all SRAM X-5 through X-9 cranks are now nominally 10 speed but each line includes 9 speed rear derailleurs so they should work fine for you.