Flashing question mark on startup

Brand new here, apologies if this has been asked before.

Whilst casually browsing on my MacBook Pro this evening (mid 2010 model) it decided to freeze for basically the first time ever. After leaving it alone for 20 minutes with no change, I held down startup button and turned it off, and back on.

Upon startup a flashing folder with a question mark in it appeared. From googling I u durst and it can't find startup disk. Holding option key brings up 'Internet recovery' option only.

Have tried this, and am now in disk utility. Unsure where to go from here.

Upon clicking 'first aid>verify disk' it tells me the Mac OSX Base System appears to be OK. Does this mean my hard drive hasn't died. I do not get the option to repair disk so have no idea where to go from here. Only time machine back up I have is months old so would prefer to avoid this if possible.

Any help much appreciated!

 

Repair disk is greyed out and unavailable?

 

Sorry for sounding like a complete idiot, but how do I boot it to anything but Internet recovery if that's the only option it gives me?

 

Thank you so much everyone for your replies. Think I may give up and attempt to find a mac store open here on a Sunday. Attempted to select restore from time machine in the first menu but it can't find a disk to boot to so am well over my head. Mac has gone from taking 5 mins to Internet boot to over 35 so I must be irritating it to say the least. As far as my know-nothing-about-computers brain can figure it, HD must have died?