Clutch manual transmission

[2004pontvbgt6spd]

2004 Pontiac vibe GT 6-speed manual transmission. I just bought this car. It's on jack stands front tires are up, front wheel drive. Scenario: without touching the clutch pedal I can go from reverse to first through 4th. In any of those gears I can get the RPMs up to 7,000 rpm then I have to engage the clutch to get into 5th and 6th gear. TIA for any information.
UPDATE: While it's running I can shift in any gear but 5th and 6th without the clutch depressed inside however underneath I can shift into gear only if the shifter is in neutral inside.

[zbyers]

What are you trying to ask? If the clutch is slipping?

https://www.youtube.com/watch?v=wlqHRxyXfqY